A077564 - OEIS

A077564

Number of partitions of n into parts with distinct prime signatures.

1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 8, 10, 10, 11, 14, 14, 19, 22, 22, 25, 30, 34, 38, 40, 46, 54, 60, 63, 74, 81, 85, 91, 108, 118, 126, 134, 153, 173, 180, 186, 214, 236, 245, 262, 301, 326, 338, 355, 395, 437, 461, 476, 540, 592, 610, 649, 717, 768, 811, 853, 943, 1039

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OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..62.

EXAMPLE

a(7) = 4. The partitions are 7, 6+1, 4+3, 4+2+1. (5+2, 3+2+2, ... are not counted.)

MATHEMATICA

sig[n_] := Sort[Last/@FactorInteger[n]]; f[n_, m_] := Module[{sm}, If[n>m(m+1)/2||n<0, Return[{}]]; If[n==0, Return[{{}}]]; sm=sig[m]; f[n, m]=Union[f[n, m-1], Prepend[ #, m]&/@Select[f[n-m, m-1], !MemberQ[sig/@#, sm]&]]]; a[n_] := Length[f[n, n]] (* f[n, m] is list of partitions of n into parts <= m with distinct prime signatures *)

CROSSREFS

Cf. A077563.

Sequence in context: A363336 A104410 A018048 * A088044 A351908 A029051

Adjacent sequences: A077561 A077562 A077563 * A077565 A077566 A077567

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Nov 11 2002

EXTENSIONS

Edited by Dean Hickerson, Nov 11 2002

STATUS

approved