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A293549 Expansion of Product_{k>=2} 1/(1 - x^k)^bigomega(k), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222). 10
1, 0, 1, 1, 3, 2, 6, 5, 13, 12, 23, 24, 47, 47, 82, 92, 152, 167, 265, 301, 462, 532, 779, 914, 1324, 1548, 2174, 2590, 3573, 4250, 5771, 6904, 9254, 11092, 14638, 17606, 23043, 27680, 35820, 43155, 55383, 66642, 84850, 102141, 129171, 155394, 195134, 234679, 293184, 352096, 437359 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Euler transform of A001222.

LINKS

Table of n, a(n) for n=0..50.

N. J. A. Sloane, Transforms

FORMULA

G.f.: Product_{k>=2} 1/(1 - x^k)^b(k), where b(k) = [x^k] Sum_{p prime, j>=1} x^(p^j)/(1 - x^(p^j)).

a(0) = 1; a(n) = (1/n)*Sum_{k=1..n} a(n-k)*b(k), b(k) = Sum_{d|k} d*bigomega(d).

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[1/(1 - x^k)^PrimeOmega[k], {k, 2, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d PrimeOmega[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 50}]

CROSSREFS

Cf. A001222, A006171, A293548.

Sequence in context: A125675 A301501 A072787 * A306443 A189073 A107271

Adjacent sequences:  A293546 A293547 A293548 * A293550 A293551 A293552

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 11 2017

STATUS

approved

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Last modified February 26 21:29 EST 2020. Contains 332295 sequences. (Running on oeis4.)