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 A281906 #4 Feb 05 2017 13:17:31
%S A281906 0,2,5,13,23,41,69,119,185,283,425,625,903,1285,1799,2517,3450,4699,
%T A281906 6340,8490,11264,14870,19485,25390,32897,42395,54372,69408,88210,
%U A281906 111612,140717,176738,221135,275776,342790,424743,524765,646420,794109,972967,1189105,1449577,1763097,2139394,2590349,3129633,3773546,4540645
%N A281906 Expansion of Sum_{p prime, i>=1} p^i*x^(p^i)/(1 - x^(p^i)) / Product_{j>=1} (1 - x^j).
%C A281906 Total sum of prime power parts (1 excluded) in all partitions of n.
%C A281906 Convolution of the sequences A000041 and A023889.
%H A281906 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A281906 G.f.: Sum_{p prime, i>=1} p^i*x^(p^i)/(1 - x^(p^i)) / Product_{j>=1} (1 - x^j).
%e A281906 a(5) = 23 because we have [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 5 + 4 + 3 + 2 + 3 + 2 + 2 + 2 = 23.
%t A281906 nmax = 48; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[i]] i x^i/(1 - x^i), {i, 2, nmax}]/Product[1 - x^j, {j, 1, nmax}], {x, 0, nmax}], x]]
%Y A281906 Cf. A000041, A023889, A066186, A073118, A246655.
%K A281906 nonn
%O A281906 1,2
%A A281906 _Ilya Gutkovskiy_, Feb 01 2017