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A263432 Number of partitions of n into divisors of n with at most one 1.

%I A263432 #27 Oct 19 2015 03:10:36
%S A263432 1,1,1,2,1,4,1,4,2,4,1,17,1,4,4,10,1,24,1,24,4,4,1,126,2,4,5,30,1,171,
%T A263432 1,36,4,4,4,490,1,4,4,251,1,290,1,43,42,4,1,1822,2,50,4,50,1,462,4,
%U A263432 421,4,4,1,13284,1,4,49,202,4,616,1,63,4,581
%N A263432 Number of partitions of n into divisors of n with at most one 1.
%C A263432 a(n) is also the number of ways to partition a group of order n into its center and its nontrivial conjugacy classes. That is, the number of possible sums in the class equation.
%D A263432 D. S. Dummit and R. M. Foote, Abstract Algebra, Wiley, 3rd edition 2003, page 124.
%H A263432 Alois P. Heinz, <a href="/A263432/b263432.txt">Table of n, a(n) for n = 1..10000</a>
%F A263432 a(n) is the coefficient of x^n in the expansion of (1 + x)/Product_{d>1,d divides n} (1 - x^d).
%e A263432 a(15) = 4 because we have: [15], [5,5,5], [5,3,3,3,1], [3,3,3,3,3].
%p A263432 with(numtheory):
%p A263432 a:= proc(n) local b, l; l:= sort([(divisors(n) minus {1})[]]):
%p A263432       b:= proc(m, i) option remember; `if`(m=0, 1, `if`(i<1,
%p A263432            `if`(m=1, 1, 0), b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i))))
%p A263432           end; forget(b):
%p A263432       b(n, nops(l))
%p A263432     end:
%p A263432 seq(a(n), n=1..100);  # _Alois P. Heinz_, Oct 18 2015
%t A263432 Table[d = Drop[Divisors[n], 1];Coefficient[Series[(1 + x)/Product[1 - x^d[[i]], {i, Length[d]}], {x, 0, n}], x,n], {n, 70}]
%Y A263432 Cf. A018818, A033630, A211110.
%K A263432 nonn,look
%O A263432 1,4
%A A263432 _Geoffrey Critzer_, Oct 18 2015