A066874 Number of partitions of n into unitary divisors of n.

1, 2, 2, 2, 2, 8, 2, 2, 2, 11, 2, 12, 2, 14, 14, 2, 2, 17, 2, 17, 18, 20, 2, 20, 2, 23, 2, 22, 2, 742, 2, 2, 26, 29, 26, 27, 2, 32, 30, 29, 2, 1654, 2, 32, 32, 38, 2, 36, 2, 41, 38, 37, 2, 44, 38, 38, 42, 47, 2, 3004, 2, 50, 42, 2, 44, 5257, 2, 47, 50, 5066, 2, 47, 2, 59, 54, 52, 50

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10001 (first 329 terms by Antti Karttunen)

David A. Corneth, PARI program

Example

a(12) = 12 because the unitary divisors of 12 are 1, 3, 4 and 12; and the partitions are 12, 4+4+4, 4+4+3+1, 4+4+(4x1), 4+3+3+1+1, 4+3+(5x1), 4+(8x1), 3+3+3+3, 3+3+3+1+1+1, 3+3+(6x1), 3+(9x1) and 12x1.

Prog

(PARI)
unitary_divisors(n) = select(d -> (1==gcd(d, n/d)), divisors(n));
partitions_into(n, parts, from=1) = if(!n, 1, my(k = #parts, s=0); for(i=from, k, if(parts[i]<=n, s += partitions_into(n-parts[i], parts, i))); (s));
A066874(n) = partitions_into(n, vecsort(unitary_divisors(n), , 4)); \\ Antti Karttunen, Aug 06 2018
(PARI) See Corneth link. \\ David A. Corneth, Aug 12 2018

Crossrefs

Cf. A018818, A034444, A077610, A285614, A286852.

Sequence in context: A337358 A295557 A327641 * A087577 A323741 A168281

Adjacent sequences: A066871 A066872 A066873 * A066875 A066876 A066877

Keyword

easy,nonn

Author

Naohiro Nomoto, Jan 26 2002

Extensions

More terms from David Wasserman, Nov 21 2002

Status

approved