A281668 - OEIS

%I #4 Jan 27 2017 13:07:07

%S 0,1,1,1,3,2,5,3,8,7,10,12,13,20,18,26,25,36,34,45,47,59,62,71,82,91,

%T 105,112,132,143,163,174,201,220,244,266,298,327,362,388,437,470,521,

%U 558,621,671,733,788,864,938,1011,1100,1182,1295,1379,1501,1606,1753,1861,2017,2158,2335,2493,2672,2871,3078

%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 distinct prime power parts (1 excluded).

%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(10) = 7 because we have [8, 2], [7, 3], [5, 3, 2] and 2 + 2 + 3 = 7.

%t nmax = 66; 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. A015723, A024938, A054685, A246655, A281616.

%K nonn

%O 1,5

%A _Ilya Gutkovskiy_, Jan 26 2017