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Search: id:A072984
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| A072984 |
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Least k such that prime(n) appears in the factorization of A001008(k) (the numerator of the k-th harmonic number). |
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6
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| 2, 4, 6, 3, 12, 16, 18, 22, 13, 30, 17, 40, 13, 46, 22, 58, 10, 66, 70, 72, 78, 82, 88, 11, 100, 102, 106, 25, 112, 126, 130, 5, 138, 148, 150, 156, 162, 166, 71, 178, 180, 190, 192, 196, 38, 210, 222, 22, 228, 232, 238, 240, 250, 66, 262, 33, 58, 276, 280, 282
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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a(n)<=n for n =2,5,14,18,25,29,33,46,49,...
For p = prime(n), Boyd defines Jp to be the set of numbers k such that p divides A001008(k). This sequence gives the least number in Jp. - T. D. Noe (noe(AT)sspectra.com), Feb 20 2004
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REFERENCES
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David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302.
A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 2..1000
David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, s=1; while(numerator(sum(k=1, s, 1/k))%prime(n)>0, s++); s)
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CROSSREFS
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Cf. A092101 (harmonic primes), A092102 (non-harmonic primes), A092103 (size of Jp).
Sequence in context: A122280 A057063 A002849 this_sequence A018841 A138125 A098793
Adjacent sequences: A072981 A072982 A072983 this_sequence A072985 A072986 A072987
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 21 2002
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