A014649 Number of partitions of n into its nonprime power divisors with at least one part of size 1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 15, 1, 1, 1, 1, 1, 16, 1, 1, 1, 6, 1, 21, 1, 2, 3, 1, 1, 26, 1, 5, 1, 2, 1, 18, 1, 6, 1, 1, 1, 238, 1, 1, 3, 1, 1, 31, 1, 2, 1, 31, 1, 139, 1, 1, 5, 2, 1, 37, 1, 26, 1, 1, 1, 414, 1, 1, 1, 6, 1, 612, 1, 2, 1, 1

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• David A. Corneth & Antti Karttunen, PARI program

Crossrefs

Cf. A014648, A014650, A014651, A014652, A066874.

Programs

PARI

\\ This is for computing a small number of terms:
nonprimepower_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)));
A014649(n) = partitions_into_with_trailing_ones(n-1, nonprimepower_divisors_with1_reversed(n)); \\ Antti Karttunen, Aug 23 2019

PARI

\\ For an efficient program to compute large numbers of terms, see PARI program included in the Links-section.