Class information for:
Level 1: PERFECT NUMBER//ODD PERFECT NUMBERS//SOCIABLE NUMBERS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
27534 227 11.9 25%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
205 3       MATHEMATICS//JOURNAL OF NUMBER THEORY//ACTA ARITHMETICA 52461
1206 2             ACTA ARITHMETICA//JOURNAL OF NUMBER THEORY//MATHEMATICS 9179
27534 1                   PERFECT NUMBER//ODD PERFECT NUMBERS//SOCIABLE NUMBERS 227

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 PERFECT NUMBER authKW 2499403 11% 77% 24
2 ODD PERFECT NUMBERS authKW 1345171 4% 100% 10
3 SOCIABLE NUMBERS authKW 1345171 4% 100% 10
4 SUM OF DIVISORS authKW 1315917 7% 65% 15
5 AMICABLE NUMBERS authKW 1210654 4% 100% 9
6 NEAR PERFECT NUMBER authKW 941619 3% 100% 7
7 AMICABLE PAIR authKW 717419 4% 67% 8
8 DEFICIENT NUMBERS authKW 672585 2% 100% 5
9 ALIQUOT SEQUENCES authKW 538068 2% 100% 4
10 ALIQUOT CYCLES authKW 480415 2% 71% 5

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 6174 70% 0% 160
2 Mathematics, Applied 1709 35% 0% 79
3 History & Philosophy of Science 806 7% 0% 15
4 Mathematics, Interdisciplinary Applications 124 6% 0% 13
5 COMPUTER APPLICATIONS & CYBERNETICS 50 0% 0% 1
6 Logic 33 1% 0% 2
7 Philosophy 21 2% 0% 4
8 Statistics & Probability 6 2% 0% 4
9 Humanities, Multidisciplinary 2 0% 0% 1
10 Religion 1 0% 0% 1

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MOSCOW LRI 134517 0% 100% 1
2 MODELING ANAL SIMULAT 67258 0% 50% 1
3 PHILOSOPH EPISTEMOL STUDIES 44838 0% 33% 1
4 MATH COMPUTAC 22418 0% 17% 1
5 UP A5028 22418 0% 17% 1
6 JV PONCELET 14539 1% 5% 2
7 MSCS 6724 0% 5% 1
8 ATER 4802 0% 4% 1
9 CNRS UMR 6205 4074 0% 3% 1
10 MATH 2046 36% 0% 81

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MATHEMATICS OF COMPUTATION 81463 22% 1% 49
2 HISTORIA MATHEMATICA 26512 4% 2% 10
3 JOURNAL OF NUMBER THEORY 15137 10% 0% 23
4 FIBONACCI QUARTERLY 14231 5% 1% 11
5 AMERICAN MATHEMATICAL MONTHLY 9748 6% 1% 14
6 INTERNATIONAL JOURNAL OF NUMBER THEORY 9711 4% 1% 9
7 BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 7930 6% 0% 14
8 PORTUGALIAE MATHEMATICA 7421 1% 2% 3
9 COLLOQUIUM MATHEMATICUM 5024 2% 1% 5
10 RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA 3385 1% 1% 3

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 PERFECT NUMBER 2499403 11% 77% 24 Search PERFECT+NUMBER Search PERFECT+NUMBER
2 ODD PERFECT NUMBERS 1345171 4% 100% 10 Search ODD+PERFECT+NUMBERS Search ODD+PERFECT+NUMBERS
3 SOCIABLE NUMBERS 1345171 4% 100% 10 Search SOCIABLE+NUMBERS Search SOCIABLE+NUMBERS
4 SUM OF DIVISORS 1315917 7% 65% 15 Search SUM+OF+DIVISORS Search SUM+OF+DIVISORS
5 AMICABLE NUMBERS 1210654 4% 100% 9 Search AMICABLE+NUMBERS Search AMICABLE+NUMBERS
6 NEAR PERFECT NUMBER 941619 3% 100% 7 Search NEAR+PERFECT+NUMBER Search NEAR+PERFECT+NUMBER
7 AMICABLE PAIR 717419 4% 67% 8 Search AMICABLE+PAIR Search AMICABLE+PAIR
8 DEFICIENT NUMBERS 672585 2% 100% 5 Search DEFICIENT+NUMBERS Search DEFICIENT+NUMBERS
9 ALIQUOT SEQUENCES 538068 2% 100% 4 Search ALIQUOT+SEQUENCES Search ALIQUOT+SEQUENCES
10 ALIQUOT CYCLES 480415 2% 71% 5 Search ALIQUOT+CYCLES Search ALIQUOT+CYCLES

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 GUO, XY , GENG, GH , LEI, DL , (2016) A NOTE ON AMICABLE NUMBERS AND THEIR VARIATIONS.PERIODICA MATHEMATICA HUNGARICA. VOL. 72. ISSUE 2. P. 180 -185 8 100% 0
2 NIELSEN, PP , (2015) ODD PERFECT NUMBERS, DIOPHANTINE EQUATIONS, AND UPPER BOUNDS.MATHEMATICS OF COMPUTATION. VOL. 84. ISSUE 295. P. 2549 -2567 9 82% 0
3 TANG, M , MA, XY , FENG, M , (2016) ON NEAR-PERFECT NUMBERS.COLLOQUIUM MATHEMATICUM. VOL. 144. ISSUE 2. P. 157 -188 7 100% 0
4 NIELSEN, PP , (2007) ODD PERFECT NUMBERS HAVE AT LEAST NINE DISTINCT PRIME FACTORS.MATHEMATICS OF COMPUTATION. VOL. 76. ISSUE 260. P. 2109-2126 10 83% 13
5 KOBAYASHI, M , POLLACK, P , POMERANCE, C , (2009) ON THE DISTRIBUTION OF SOCIABLE NUMBERS.JOURNAL OF NUMBER THEORY. VOL. 129. ISSUE 8. P. 1990-2009 8 100% 1
6 BAISHYA, SJ , DAS, AK , (2014) HARMONIC NUMBERS AND FINITE GROUPS.RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA. VOL. 132. ISSUE . P. 33 -43 7 100% 0
7 GALLARDO, LH , RAHAVANDRAINY, O , (2012) ALL UNITARY PERFECT POLYNOMIALS OVER F-2 WITH AT MOST FOUR DISTINCT IRREDUCIBLE FACTORS.JOURNAL OF SYMBOLIC COMPUTATION. VOL. 47. ISSUE 4. P. 492-502 7 100% 0
8 LI, YB , LIAO, QY , (2015) A CLASS OF NEW NEAR-PERFECT NUMBERS.JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY. VOL. 52. ISSUE 4. P. 751 -763 6 100% 1
9 GOTO, T , OHNO, Y , (2008) ODD PERFECT NUMBERS HAVE A PRIME FACTOR EXCEEDING 10(8).MATHEMATICS OF COMPUTATION. VOL. 77. ISSUE 263. P. 1859 -1868 8 89% 4
10 MARQUES, D , SCHLEISCHITZ, J , (2016) ON A PROBLEM POSED BY MAHLER.JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. VOL. 100. ISSUE 1. P. 86 -107 8 73% 0

Classes with closest relation at Level 1


Rank Class id link
1 14037 CARMICHAEL NUMBERS//PRIMALITY TESTING//PSEUDOPRIME
2 19793 PRIMES IN RESIDUE CLASSES//CHEBYSHEVS BIAS//FACTORIZATIONS OF DISTINCT LENGTHS
3 33449 POLYADIC GROUPS//WARINGS PROBLEM//N M SEMIGROUP
4 36033 COMMUNIST AND POST COMMUNIST STUDIES//MANDATORY RESETTLEMENT//MEMORIAL MOVEMENT
5 19204 HISTORIA MATHEMATICA//BOLLETTINO DI STORIA DELLE SCIENZE MATEMATICHE//ARCHIVE FOR HISTORY OF EXACT SCIENCES
6 21072 SCHUR MULTIPLIER//COMMUTATIVITY DEGREE//NON ABELIAN TENSOR SQUARE
7 13744 EGYPTIAN FRACTIONS//COMP ALGEBRA//MULTIPLICATIVE FUNCTIONS
8 30184 BIPARTITE SELF COMPLEMENTARY GRAPH//MATRIX SYMMETRIZATION//NEXUS NETWORK JOURNAL
9 13837 SUM PRODUCT ESTIMATES//FERMAT QUOTIENTS//DISTINCT DISTANCES
10 21795 ARCHIVE FOR HISTORY OF EXACT SCIENCES//HISTORIA MATHEMATICA//HYPERREALS

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