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A294266
Number of partitions of n into distinct squares that do not divide n.
4
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
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
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Oct 26 2017
STATUS
approved