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A066874 Number of partitions of n into unitary divisors of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A270379 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

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Last modified October 22 04:25 EDT 2019. Contains 328315 sequences. (Running on oeis4.)