A284833 Expansion of Sum_{i>=1} x^prime(i)/(1 - x^prime(i)) * Product_{j=1..i} 1/(1 - x^prime(j)).

0, 1, 1, 2, 2, 5, 3, 7, 6, 11, 8, 17, 12, 22, 21, 28, 27, 41, 35, 53, 52, 66, 66, 90, 85, 112, 114, 140, 143, 182, 180, 219, 236, 269, 291, 342, 353, 417, 444, 508, 540, 625, 657, 751, 812, 901, 974, 1097, 1168, 1313, 1414, 1562, 1684, 1874, 2008, 2219, 2397, 2626, 2832, 3121, 3341, 3668, 3956, 4305, 4650

Offset: 1

Author

Ilya Gutkovskiy, Apr 03 2017

Keywords

• nonn

Comments

Total number of largest parts in all partitions of n into prime parts.

Examples

			a(10) = 11 because we have [7, 3], [5, 5], [5, 3, 2], [3, 3, 2, 2], [2, 2, 2, 2, 2] and 1 + 2 + 1 + 2 + 5 = 11.
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000607, A046746, A084993, A092311, A281544, A284827.

Programs

Mathematica

nmax = 65; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]

PARI

x='x+O('x^66); concat([0], Vec(sum(i=1, 66, x^prime(i)/(1 - x^prime(i)) * prod(j=1,i, 1/(1 - x^prime(j)))))) \\ Indranil Ghosh, Apr 04 2017

Formula

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