A197132 Euler transform of composite numbers.

1, 4, 16, 52, 157, 434, 1144, 2862, 6906, 16090, 36449, 80430, 173555, 366802, 761102, 1552569, 3118508, 6174461, 12064383, 23283027, 44419855, 83834278, 156626605, 289839251, 531534746, 966483534, 1743164649, 3119864511, 5543030861, 9779552117, 17139055493

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Transforms

Formula

G.f.: Product_{k>=1} (1-x^k)^-composite(k), where composite(k) = A002808(k) is the k-th composite number.

Maple

N:= 100: # to use composites <= N
comps:= remove(isprime, [$4..N]):
M:= nops(comps):
G:= mul((1-x^k)^(-comps[k]), k=1..M):
S:= series(G, x, M+1):
seq(coeff(S, x, j), j=0..M); # Robert Israel, Jan 30 2018

Mathematica

a[ns_Integer?NonNegative, nf_Integer?NonNegative] := CoefficientList[Series[Product[(1 - x^k)^-FixedPoint[k + PrimePi[#] + 1 &, k], {k, 1, nf}], {x, 0, nf}], x][[ns + 1 ;; nf + 1]]; a[0, 30] (* Robert P. P. McKone, Nov 08 2023 *)

Crossrefs

Cf. A002808, A030009.

Sequence in context: A188125 A007688 A320237 * A266943 A100774 A336994

Adjacent sequences: A197129 A197130 A197131 * A197133 A197134 A197135

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 10 2011

Status

approved