A120352 Numerator of Sum[ 1/k^p, {k,1,p-1} ], where p = Prime[n].

1, 9, 257875, 940908897061, 26038773205374138944970092886340352227, 5706439637514064062030256049808675747470805004854626598761, 3819751175863358416058062379293843331497647520922258560223903226691067255782388923965399403291707829

Offset

1,2

Comments

p^3 divides a(n) for n>2. A119722[n] = a(n)/p^3, p=Prime[n].

Numerators of Sum[ 1/k^n, {k,1,n-1} ] are listed in A120347(n) = {1, 9, 1393, 257875, 47463376609, 940908897061, ...}.

Links

Table of n, a(n) for n=1..7.

Formula

a(n) = Numerator[ Sum[ 1/k^Prime[n], {k,1,Prime[n]-1} ]]. a(n) = Numerator[ Zeta[p] - Zeta[p,p] ], for p = Prime[n].

a(n) = A120347[ Prime[n] ].

Mathematica

Table[Numerator[Sum[1/k^Prime[n], {k, 1, Prime[n]-1}]], {n, 1, 8}]

Crossrefs

Cf. A119722.

Cf. A120347.

Sequence in context: A300195 A368068 A159344 * A225069 A058468 A133414

Adjacent sequences: A120349 A120350 A120351 * A120353 A120354 A120355

Keyword

frac,nonn

Author

Alexander Adamchuk, Aug 16 2006, Oct 31 2006

Status

approved