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A293548 Expansion of Product_{k>=2} 1/(1 - x^k)^omega(k), where omega(k) is the number of distinct primes dividing k (A001221). 13
1, 0, 1, 1, 2, 2, 5, 4, 8, 9, 15, 16, 28, 29, 46, 54, 77, 90, 131, 150, 211, 251, 337, 401, 540, 637, 839, 1006, 1296, 1551, 1995, 2373, 3013, 3610, 4523, 5410, 6754, 8045, 9965, 11897, 14614, 17410, 21313, 25316, 30816, 36615, 44307, 52539, 63387, 74975, 90078 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Euler transform of A001221.
LINKS
N. J. A. Sloane, Transforms
FORMULA
G.f.: Product_{k>=2} 1/(1 - x^k)^b(k), where b(k) = [x^k] Sum_{j>=1} x^prime(j)/(1 - x^prime(j)).
a(0) = 1; a(n) = (1/n)*Sum_{k=1..n} a(n-k)*b(k), b(k) = Sum_{d|k} d*omega(d).
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[1/(1 - x^k)^PrimeNu[k], {k, 2, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d PrimeNu[d], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 50}]
CROSSREFS
Sequence in context: A206556 A127683 A127686 * A318844 A034400 A021820
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 11 2017
STATUS
approved

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Last modified February 21 04:30 EST 2024. Contains 370219 sequences. (Running on oeis4.)