login
Number of partitions of n into distinct parts of order n.
11

%I #12 Dec 19 2018 15:12:06

%S 1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,3,1,2,1,1,1,4,1,1,1,2,1,4,1,1,1,1,

%T 1,6,1,1,1,3,1,3,1,1,1,1,1,6,1,1,1,1,1,4,1,2,1,1,1,32,1,1,1,1,1,3,1,1,

%U 1,1,1,25,1,1,1,1,1,2,1,4,1,1,1,24,1,1,1,2,1,24,1,1,1,1,1,12,1,1,1,3,1,2

%N Number of partitions of n into distinct parts of order n.

%C Order of partition is lcm of its parts.

%H Antti Karttunen, <a href="/A074971/b074971.txt">Table of n, a(n) for n = 1..16384</a>

%F Coefficient of x^n in expansion of Sum_{i divides n} mu(n/i)*Product_{j divides i} (1+x^j).

%e The a(36) = 6 partitions are (36), (18,12,6), (18,12,4,2), (18,12,3,2,1), (18,9,4,3,2), (12,9,6,4,3,2). - _Gus Wiseman_, Aug 01 2018

%o (PARI) A074971(n) = { my(q=0); fordiv(n,i,my(p=1); fordiv(i,j,p *= (1 + 'x^j)); q += moebius(n/i)*p); polcoeff(q,n); }; \\ _Antti Karttunen_, Dec 19 2018

%Y Cf. A000837, A074761, A285572, A290103, A305566, A316431, A316433, A317624.

%Y Cf. also A033630.

%K nonn

%O 1,6

%A _Vladeta Jovovic_, Oct 05 2002