A294266 Number of partitions of n into distinct squares that do not divide n.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 3, 0, 0, 0, 1, 1, 0, 0, 1, 3, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 3, 1, 0, 0, 2, 3, 0, 0, 1, 1, 0, 1, 2, 1, 1, 0, 2, 2, 0, 0, 3, 4

Offset: 0

Author

Ilya Gutkovskiy, Oct 26 2017

Keywords

• nonn
• look

Examples

			a(29) = 2 because we have [25, 4] and [16, 9, 4].
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to partitions
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A033461, A200745, A284345, A294265, A371968.

Programs

Maple

f:= proc(n) local P,k,x;
P:= 1;
for k from 2 to floor(sqrt(n)) do
  if n mod k^2 = 0 then next fi;
  P:= series(P*(1+x^(k^2)),x,n+1);
od;
coeff(P,x,n)
end proc:
map(f, [$0..200]); # Robert Israel, Apr 15 2024

Mathematica

Table[SeriesCoefficient[Product[1 + Boole[Mod[n, k] > 0 && OddQ[DivisorSigma[0, k]]] x^k, {k, 1, n}], {x, 0, n}], {n, 0, 110}]