A014650 Number of partitions of n into its divisors that are powers of primes (A000961) with at least one part of size 1.

1, 1, 1, 2, 1, 5, 1, 6, 3, 8, 1, 27, 1, 11, 11, 26, 1, 43, 1, 63, 15, 17, 1, 215, 5, 20, 18, 114, 1, 226, 1, 166, 23, 26, 23, 734, 1, 29, 27, 728, 1, 422, 1, 261, 181, 35, 1, 2697, 7, 179, 35, 357, 1, 791, 35, 1729, 39, 44, 1, 6747, 1, 47, 325, 1626, 41, 996, 1, 594, 47, 1062, 1, 20345, 1, 56, 327, 735, 47, 1374, 1, 13485, 216, 62, 1

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• David A. Corneth, PARI program

Crossrefs

Cf. A000961, A014648, A014649, A014651, A014652, A066874.

Programs

PARI

\\ This is for computing a small number of terms:
primepower_divisors_with1_reversed(n) = vecsort(select(d -> ((1==d) || isprimepower(d)), divisors(n)), , 4);
partitions_into_with_trailing_ones(n,parts,from=1) = if(!n,1, if(#parts<=(from+1), if(#parts == from,1,(1+(n\parts[from]))), my(s=0); for(i=from,#parts,if(parts[i]<=n, s += partitions_into_with_trailing_ones(n-parts[i],parts,i))); (s)));
A014650(n) = partitions_into_with_trailing_ones(n-1,primepower_divisors_with1_reversed(n)); \\ Antti Karttunen, Sep 10 2018

PARI

\\ For an efficient program to compute large numbers of terms, see David A. Corneth's PARI program included in the Links-section. - Antti Karttunen, Sep 12 2018

Extensions

More terms from and the name clarified by Antti Karttunen, Sep 10 2018