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A066874
Number of partitions of n into unitary divisors of n.
9
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
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 26 2002
EXTENSIONS
More terms from David Wasserman, Nov 21 2002
STATUS
approved