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Number of partitions of n into distinct squares that do not divide n.
4

%I #13 Apr 16 2024 10:45:30

%S 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,

%T 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,

%U 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

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

%H Robert Israel, <a href="/A294266/b294266.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

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

%p f:= proc(n) local P,k,x;

%p P:= 1;

%p for k from 2 to floor(sqrt(n)) do

%p if n mod k^2 = 0 then next fi;

%p P:= series(P*(1+x^(k^2)),x,n+1);

%p od;

%p coeff(P,x,n)

%p end proc:

%p map(f, [$0..200]); # _Robert Israel_, Apr 15 2024

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

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

%K nonn,look

%O 0,30

%A _Ilya Gutkovskiy_, Oct 26 2017