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

0,7

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?

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A077564.

Sequence in context: A329493 A139821 A248972 * A055256 A369985 A295630

Adjacent sequences: A077560 A077561 A077562 * A077564 A077565 A077566

Keyword

nonn

Author

Amarnath Murthy, Nov 11 2002

Extensions

Edited by Dean Hickerson, Nov 11 2002

Status

approved