cp's OEIS Frontend

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

%I A066874 #23 Aug 24 2018 10:33:04
%S A066874 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 A066874 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 A066874 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 A066874 Number of partitions of n into unitary divisors of n.
%H A066874 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 A066874 David A. Corneth, <a href="/A066874/a066874.gp.txt">PARI program</a>
%e A066874 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 A066874 (PARI)
%o A066874 unitary_divisors(n) = select(d -> (1==gcd(d,n/d)), divisors(n));
%o A066874 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 A066874(n) = partitions_into(n,vecsort(unitary_divisors(n), , 4)); \\ _Antti Karttunen_, Aug 06 2018
%o A066874 (PARI) See Corneth link. \\ _David A. Corneth_, Aug 12 2018
%Y A066874 Cf. A018818, A034444, A077610, A285614, A286852.
%K A066874 easy,nonn
%O A066874 1,2
%A A066874 _Naohiro Nomoto_, Jan 26 2002
%E A066874 More terms from _David Wasserman_, Nov 21 2002