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

Author

Naohiro Nomoto, Jan 26 2002

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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

Extensions

More terms from David Wasserman, Nov 21 2002