cp's OEIS Frontend

A161148 Number of partitions of n such that each term of the partition is a squared divisor of n.

%I A161148 #8 Apr 04 2024 10:05:36
%S A161148 1,1,1,2,1,2,1,3,2,3,1,5,1,4,2,6,1,9,1,8,3,6,1,16,2,7,4,12,1,21,1,15,
%T A161148 4,9,2,39,1,10,5,25,1,35,1,24,9,12,1,76,2,21,6,32,1,61,3,38,7,15,1,
%U A161148 174,1,16,10,46,3,93,1,50,8,42,1,231,1,19,19,60,2,135,1
%N A161148 Number of partitions of n such that each term of the partition is a squared divisor of n.
%F A161148 a(p) = 1 if p a prime (A000040).
%F A161148 a(2p) = A130291(n) if p=A000040(n).
%F A161148 a(n) = [x^n] Product_{d|n} 1/( 1-x^(d^2) ).
%e A161148 a(n=12)=5 counts these 5 partitions of 12: 1^2+1^2+..+1^2 = 1^2+1^2+...+1^2+2^2 = 1^2+1^2+..+1^2+2^2+2^2 = 1^2+1^2+1^2+3^2=2^2+2^2+2^2. Partitions with the divisors 4, 6 or 12 do not contribute to the count because 4^2, 6^2 and 12^2 are larger than n.
%p A161148 a := proc(n) coeftayl(1/mul(1-x^(d^2),d=numtheory[divisors](n)),x=0,n) ; end:
%t A161148 a[n_] := SeriesCoefficient[1/Product[1-x^(d^2), {d, Divisors[n]}], {x, 0, n}];
%t A161148 Table[a[n], {n, 1, 80}] (* _Jean-François Alcover_, Apr 04 2024, after Maple code *)
%Y A161148 Cf. A000040, A130291, A018818, A001156, A002635.
%K A161148 nonn
%O A161148 1,4
%A A161148 _R. J. Mathar_, Jun 03 2009