This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A281616 #6 Jan 27 2017 13:06:32
%S A281616 0,1,1,3,3,7,8,15,18,28,36,53,66,91,117,156,195,254,318,407,503,630,
%T A281616 777,965,1176,1439,1750,2124,2559,3078,3692,4417,5257,6246,7405,8753,
%U A281616 10314,12127,14233,16668,19464,22687,26406,30662,35539,41109,47495,54767,63044,72454,83167,95305,109054,124607,142209,162076,184464
%N A281616 Expansion of Sum_{p prime, i>=1} x^(p^i)/(1 - x^(p^i)) / Product_{p prime, j>=1} (1 - x^(p^j)).
%C A281616 Total number of parts in all partitions of n into prime power parts (1 excluded).
%C A281616 Convolution of A001222 and A023894.
%H A281616 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A281616 G.f.: Sum_{p prime, i>=1} x^(p^i)/(1 - x^(p^i)) / Product_{p prime, j>=1} (1 - x^(p^j)).
%e A281616 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 A281616 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 A281616 Cf. A001222, A023894, A084993, A246655.
%K A281616 nonn
%O A281616 1,4
%A A281616 _Ilya Gutkovskiy_, Jan 25 2017