A281668 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, 1, 3, 2, 5, 3, 8, 7, 10, 12, 13, 20, 18, 26, 25, 36, 34, 45, 47, 59, 62, 71, 82, 91, 105, 112, 132, 143, 163, 174, 201, 220, 244, 266, 298, 327, 362, 388, 437, 470, 521, 558, 621, 671, 733, 788, 864, 938, 1011, 1100, 1182, 1295, 1379, 1501, 1606, 1753, 1861, 2017, 2158, 2335, 2493, 2672, 2871, 3078

Offset: 1

Author

Ilya Gutkovskiy, Jan 26 2017

Keywords

• nonn

Comments

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

Examples

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

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A015723, A024938, A054685, A246655, A281616.

Programs

Mathematica

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]]

Formula

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