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 A120285 Numerator of harmonic number H(p-1) = Sum_{k=1..p-1} 1/k for prime p. 2
 1, 3, 25, 49, 7381, 86021, 2436559, 14274301, 19093197, 315404588903, 9304682830147, 54801925434709, 2078178381193813, 12309312989335019, 5943339269060627227, 14063600165435720745359, 254381445831833111660789 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Prime(n)^2 divides a(n) for n>2. LINKS Robert Israel, Table of n, a(n) for n = 1..342 R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057 [math.NT], 2011. Eric Weisstein's World of Mathematics, Wolstenholme's Theorem. FORMULA a(n) = numerator(Sum_{k=1..prime(n)-1} 1/k). a(n) = A001008(prime(n)-1). a(n) = A061002(n)*prime(n)^2 for n > 2. 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)]; MATHEMATICA Numerator[Table[Sum[1/k, {k, 1, Prime[n]-1}], {n, 1, 20}]] Table[HarmonicNumber[p], {p, Prime[Range[20]]-1}]//Numerator (* Harvey P. Dale, May 18 2023 *) PROG (PARI) a(n) = my(p=prime(n)); numerator(sum(k=1, p-1, 1/k)); \\ Michel Marcus, Dec 25 2018 CROSSREFS Cf. A001008, A061002, A185399. Sequence in context: A051280 A145609 A259923 * A041897 A356594 A242974 Adjacent sequences: A120282 A120283 A120284 * A120286 A120287 A120288 KEYWORD frac,nonn AUTHOR Alexander Adamchuk, Jul 07 2006 STATUS approved

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Last modified December 7 01:44 EST 2023. Contains 367616 sequences. (Running on oeis4.)