A281616 Expansion of Sum_{p prime, i>=1} x^(p^i)/(1 - x^(p^i)) / Product_{p prime, j>=1} (1 - x^(p^j)).

0, 1, 1, 3, 3, 7, 8, 15, 18, 28, 36, 53, 66, 91, 117, 156, 195, 254, 318, 407, 503, 630, 777, 965, 1176, 1439, 1750, 2124, 2559, 3078, 3692, 4417, 5257, 6246, 7405, 8753, 10314, 12127, 14233, 16668, 19464, 22687, 26406, 30662, 35539, 41109, 47495, 54767, 63044, 72454, 83167, 95305, 109054, 124607, 142209, 162076, 184464

Offset: 1

Author

Ilya Gutkovskiy, Jan 25 2017

Keywords

• nonn

Comments

Total number of parts in all partitions of n into prime power parts (1 excluded).

Convolution of A001222 and A023894.

Examples

			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.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A001222, A023894, A084993, A246655.

Programs

Mathematica

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]]

Formula

G.f.: Sum_{p prime, i>=1} x^(p^i)/(1 - x^(p^i)) / Product_{p prime, j>=1} (1 - x^(p^j)).