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A014650 Number of partitions of n into its divisors that are powers of primes (A000961) with at least one part of size 1. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

David A. Corneth, PARI program

PROG

(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

CROSSREFS

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

Sequence in context: A151737 A211361 A249548 * A014648 A260147 A263454

Adjacent sequences:  A014647 A014648 A014649 * A014651 A014652 A014653

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

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

STATUS

approved

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Last modified July 11 15:58 EDT 2020. Contains 335626 sequences. (Running on oeis4.)