cp's OEIS Frontend

A294105 Number of compositions (ordered partitions) of n into squares dividing n.

%I A294105 #22 Oct 30 2017 19:50:07
%S A294105 1,1,1,1,2,1,1,1,7,2,1,1,26,1,1,1,96,1,12,1,345,1,1,1,1252,2,1,76,
%T A294105 4544,1,1,1,17473,1,1,1,127654,1,1,1,217286,1,1,1,788674,2490,1,1,
%U A294105 3182706,2,28,1,10390321,1,14128,1,37713313,1,1,1,136886433,1,1,80396,579739960,1,1,1,1803399103,1,1
%N A294105 Number of compositions (ordered partitions) of n into squares dividing n.
%H A294105 Alois P. Heinz, <a href="/A294105/b294105.txt">Table of n, a(n) for n = 0..2500</a>
%H A294105 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H A294105 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A294105 a(8) = 7 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are squares {1, 4} therefore we have [4, 4], [4, 1, 1, 1, 1], [1, 4, 1, 1, 1], [1, 1, 4, 1, 1], [1, 1, 1, 4, 1], [1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1].
%p A294105 a:= proc(n) option remember; local b, l;
%p A294105       l, b:= select(issqr, numtheory[divisors](n)),
%p A294105       proc(m) option remember; `if`(m=0, 1,
%p A294105          add(`if`(j>m, 0, b(m-j)), j=l))
%p A294105       end; b(n)
%p A294105     end:
%p A294105 seq(a(n), n=0..50);  # _Alois P. Heinz_, Oct 30 2017
%t A294105 Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] == 0 && IntegerQ[k^(1/2)]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 70}]
%Y A294105 Cf. A006456, A046951, A100346, A284345.
%K A294105 nonn
%O A294105 0,5
%A A294105 _Ilya Gutkovskiy_, Oct 28 2017