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

0,30

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

Example

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

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}]

Crossrefs

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

Sequence in context: A089814 A063100 A353377 * A127475 A086014 A025437

Adjacent sequences: A294263 A294264 A294265 * A294267 A294268 A294269

Keyword

nonn,look,changed

Author

Ilya Gutkovskiy, Oct 26 2017

Status

approved