A120285 Numerator of harmonic number H(p-1) = Sum_{k=1..p-1} 1/k for prime p.

1, 3, 25, 49, 7381, 86021, 2436559, 14274301, 19093197, 315404588903, 9304682830147, 54801925434709, 2078178381193813, 12309312989335019, 5943339269060627227, 14063600165435720745359, 254381445831833111660789

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