A014650 - OEIS

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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.

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

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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: A211361 A347464 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