0,7

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?

Table of n, a(n) for n=0..76.

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

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

Cf. A077564.

Sequence in context: A237121 A139821 A248972 * A055256 A029147 A228571

Adjacent sequences: A077560 A077561 A077562 * A077564 A077565 A077566

nonn

Amarnath Murthy, Nov 11 2002

Edited by Dean Hickerson, Nov 11 2002

approved