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 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Jan 27 2017 13:06:32
%S 0,1,1,3,3,7,8,15,18,28,36,53,66,91,117,156,195,254,318,407,503,630,
%T 777,965,1176,1439,1750,2124,2559,3078,3692,4417,5257,6246,7405,8753,
%U 10314,12127,14233,16668,19464,22687,26406,30662,35539,41109,47495,54767,63044,72454,83167,95305,109054,124607,142209,162076,184464
%N Expansion of Sum_{p prime, i>=1} x^(p^i)/(1 - x^(p^i)) / Product_{p prime, j>=1} (1 - x^(p^j)).
%C Total number of parts in all partitions of n into prime power parts (1 excluded).
%C Convolution of A001222 and A023894.
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Sum_{p prime, i>=1} x^(p^i)/(1 - x^(p^i)) / Product_{p prime, j>=1} (1 - x^(p^j)).
%e a(9) = 18 because we have [9], [7, 2], [5, 4], [5, 2, 2], [4, 3, 2], [3, 3, 3], [3, 2, 2, 2] and 1 + 2 + 2 + 3 + 3 + 3 + 4 = 18.
%t nmax = 57; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[i]] x^i/(1 - x^i), {i, 2, nmax}]/Product[1 - Floor[1/PrimeNu[j]] x^j, {j, 2, nmax}], {x, 0, nmax}], x]]
%Y Cf. A001222, A023894, A084993, A246655.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Jan 25 2017