A077563 Number of partitions into two parts which have different prime signatures.

0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 4, 5, 6, 4, 8, 6, 8, 6, 8, 8, 11, 7, 10, 10, 12, 10, 12, 10, 13, 10, 15, 12, 15, 10, 17, 16, 17, 13, 18, 16, 18, 16, 19, 18, 21, 13, 20, 19, 25, 20, 23, 19, 24, 20, 25, 24, 27, 19, 24, 26, 28, 21, 28, 25, 30, 26, 31, 26, 32, 19, 30, 30, 33, 30

Offset: 0

Author

Amarnath Murthy, Nov 11 2002

Keywords

• nonn

Comments

The 'prime signature' of n is the sorted list of exponents in the prime factorization of n.

Does lim n->infinity a(n)/n exist? If not, what are the limsup and liminf of a(n)/n?

Examples

			a(9) = 3; the partitions are 8+1, 6+3 and 5+4.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A077564.

Programs

Mathematica

sig[n_] := Sort[Last/@FactorInteger[n]]; a[n_] := Length[Select[Range[Floor[n/2]], sig[ # ]!=sig[n-# ]&]]

Extensions

Edited by Dean Hickerson, Nov 11 2002