A120273 Absolute value of the numerator of Sum_{i=1..n} (-1)^i * i/prime(i).

1, 1, 13, 29, 731, 4357, 136141, 1497401, 52856987, 698076077, 49526267143, 574253997269, 72925181864501, 1123720869207397, 143426539122302791, 2236629947933814637, 422054527184135696827, 8864360144543549996813

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..300

Formula

a(n) = abs(numerator(Sum_{i=1..n} (-1)^i * i/prime(i))).

a(n) = abs(Sum_{i=1..n} ((i(-1)^i * (Product_{k=1..n} prime(k)))/prime(i))). - Petr Platais, Aug 14 2022

Mathematica

Abs[Numerator[Table[Sum[(-1)^i*i/Prime[i], {i, 1, n}], {n, 1, 20}]]]
Abs[Table[Sum[(m*(-1)^m*Product[Prime[n], {n, 1, k}])/Prime[m], {m, 1, k}], {k, 1, 20}]] (* Petr Platais, Aug 11 2022 *)

Prog

(PARI) for(n=1, 20, print1(numerator(abs(sum(k=1, n, (-1)^k*k/prime(k)))), ", ")) \\ G. C. Greubel, Aug 23 2018
(Magma) [Numerator(Abs((&+[(-1)^k*k/NthPrime(k): k in [0..n]]))): n in [1..20]]; // G. C. Greubel, Aug 23 2018

Crossrefs

Sequence in context: A317897 A195878 A013545 * A104817 A048450 A216193

Adjacent sequences: A120270 A120271 A120272 * A120274 A120275 A120276

Keyword

frac,nonn

Author

Alexander Adamchuk, Jul 01 2006

Status

approved