%I #23 Aug 24 2018 10:33:04

%S 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,

%T 742,2,2,26,29,26,27,2,32,30,29,2,1654,2,32,32,38,2,36,2,41,38,37,2,

%U 44,38,38,42,47,2,3004,2,50,42,2,44,5257,2,47,50,5066,2,47,2,59,54,52,50

%N Number of partitions of n into unitary divisors of n.

%H David A. Corneth, <a href="/A066874/b066874.txt">Table of n, a(n) for n = 1..10001</a> (first 329 terms by Antti Karttunen)

%H David A. Corneth, <a href="/A066874/a066874.gp.txt">PARI program</a>

%e 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.

%o (PARI)

%o unitary_divisors(n) = select(d -> (1==gcd(d,n/d)), divisors(n));

%o 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));

%o A066874(n) = partitions_into(n,vecsort(unitary_divisors(n), , 4)); \\ _Antti Karttunen_, Aug 06 2018

%o (PARI) See Corneth link. \\ _David A. Corneth_, Aug 12 2018

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

%K easy,nonn

%O 1,2

%A _Naohiro Nomoto_, Jan 26 2002

%E More terms from _David Wasserman_, Nov 21 2002