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

1,1

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).

Links

Table of n, a(n) for n=1..29.

Formula

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

Example

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

Maple

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

Crossrefs

Cf. A000040, A000041, A066186.

Sequence in context: A179079 A084449 A182144 * A176607 A134815 A367992

Adjacent sequences: A182720 A182721 A182722 * A182724 A182725 A182726

Keyword

nonn

Author

Omar E. Pol, Jan 27 2011

Status

approved