The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Cf. A001221, A006171, A293549. Sequence in context: A206556 A127683 A127686 * A318844 A034400 A021820 Adjacent sequences: A293545 A293546 A293547 * A293549 A293550 A293551 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Oct 11 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 00:42 EST 2022. Contains 358453 sequences. (Running on oeis4.)