A318367 a(n) = Sum_{d|n} (-1)^(n/d+1)*d*prime(d).

2, 4, 17, 20, 57, 67, 121, 116, 224, 239, 343, 371, 535, 487, 777, 660, 1005, 958, 1275, 1095, 1669, 1401, 1911, 1715, 2482, 2097, 3005, 2295, 3163, 2987, 3939, 3156, 4879, 3727, 5391, 4502, 5811, 4925, 7063, 5271, 7341, 6619, 8215, 6433, 9849, 7249, 9919, 8691, 11244, 9264

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{k>=1} k*prime(k)*x^k/(1 + x^k).

L.g.f.: log(Product_{k>=1} (1 + x^k)^prime(k)) = Sum_{n>=1} a(n)*x^n/n.

Maple

f:= proc(n) local d; add((-1)^(n/d+1)*d*ithprime(d), d = numtheory:-divisors(n)); end proc:map(f, [$1..100]); # Robert Israel, Aug 01 2023

Mathematica

Table[Sum[(-1)^(n/d + 1) d Prime[d], {d, Divisors[n]}], {n, 50}]
nmax = 50; Rest[CoefficientList[Series[Sum[k Prime[k] x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
nmax = 50; Rest[CoefficientList[Series[Log[Product[(1 + x^k)^Prime[k], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]

Prog

(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*d*prime(d)); \\ Michel Marcus, Aug 25 2018

Crossrefs

Cf. A033286, A061150, A061151, A061152.

Sequence in context: A254206 A118242 A006276 * A317488 A103051 A095018

Adjacent sequences: A318364 A318365 A318366 * A318368 A318369 A318370

Keyword

nonn,look

Author

Ilya Gutkovskiy, Aug 24 2018

Status

approved