A182723 Sum of (all parts of) all partitions of prime(n).

4, 9, 35, 105, 616, 1313, 5049, 9310, 28865, 132385, 212102, 800569, 1827903, 2720223, 5863438, 17486343, 49077380, 68411805, 179539163, 333501555, 451555297, 1094043350, 1937092927, 4449637325, 12923400210, 21662593726, 27938641850, 46132984623, 59072140160

Offset: 1

Author

Omar E. Pol, Jan 27 2011

Keywords

• nonn

Comments

These moments have a visualization when the shell model of partitions of A135010 is connected to the geometric model of the divisors of the natural numbers which gives the location of the prime numbers (see the illustrations of initial terms in the entries A000005, A000040 and A000041).

Examples

			a(6) = 1313 because the 6th prime is 13 and the partition number of 13 is 101, so 13*101=1313.
		

Crossrefs

Cf. A000040, A000041, A066186.

Programs

Maple

A182723 := proc(n) local p; p := ithprime(n) ; p*combinat[numbpart](p) ; end proc: # R. J. Mathar, Jan 31 2011

Formula

a(n) = A000040(n)*A000041(A000040(n)) = A066186(prime(n)).