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A120285
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Numerator of harmonic number H(p-1) = Sum[ 1/k, {k,1,p-1}] for prime p.
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1
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1, 3, 25, 49, 7381, 86021, 2436559, 14274301, 19093197, 315404588903, 9304682830147, 54801925434709, 2078178381193813, 12309312989335019, 5943339269060627227, 14063600165435720745359, 254381445831833111660789
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Prime[n]^2 divides a(n) for n>2.
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LINKS
| R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057, 2011
Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.
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FORMULA
| a(n) = numerator[Sum[1/k,{k,1,Prime[n]-1}]]. a(n) = A001008[Prime[n]-1]. a(n) = A061002[n]*Prime[n]^2 for n>2.
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MAPLE
| f3:=proc(n) local p;
p:=ithprime(n);
numer(add(1/i, i=1..p-1));
end proc;
[seq(f3(n), n=1..20)];
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MATHEMATICA
| Numerator[Table[Sum[1/k, {k, 1, Prime[n]-1}], {n, 1, 20}]]
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CROSSREFS
| Cf. A001008, A061002, A185399.
Sequence in context: A042899 A051280 A145609 * A041897 A006222 A129443
Adjacent sequences: A120282 A120283 A120284 * A120286 A120287 A120288
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KEYWORD
| frac,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 07 2006
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