OFFSET
1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
FORMULA
a(n) = Sum_{k=1..n} bigomega(k)*numbpart(n-k).
G.f.: Sum_{i>=2} floor(1/omega(i))*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j), where omega() is the number of distinct prime factors (A001221). - Ilya Gutkovskiy, Jan 24 2017
EXAMPLE
a(4)=5 because in all partitions of 4 we have 5 powers of primes (shown between parentheses): (4), (3)1, (2)(2), (2)11, 1111.
MAPLE
with(numtheory): with(combinat): a:= n-> add(bigomega(k)*numbpart(n-k), k=1..n): seq(a(n), n=1..46); # Emeric Deutsch, Feb 26 2005
MATHEMATICA
Table[Sum[PrimeOmega[k]*PartitionsP[n - k], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, May 05 2017 *)
PROG
(PARI) a(n) = sum(k=1, n, bigomega(k)*numbpart(n-k)); \\ Michel Marcus, May 05 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 22 2002
EXTENSIONS
More terms from Emeric Deutsch, Feb 26 2005
STATUS
approved