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A353645 a(1) = 1, and for n > 1, number of ways to write the square of n as a product of at least two factors, the largest two of which are equal.

%I A353645 #9 May 03 2022 16:33:14
%S A353645 1,1,1,2,1,2,1,4,2,3,1,5,1,3,2,7,1,5,1,6,2,3,1,10,2,3,4,6,1,8,1,12,3,
%T A353645 3,2,15,1,3,3,12,1,9,1,7,5,3,1,21,2,6,3,7,1,13,2,12,3,3,1,21,1,3,5,21,
%U A353645 2,11,1,8,3,7,1,35,1,3,5,8,2,12,1,23,7,3,1,25,2,3,3,15,1,21,2,8,3,3,2,43,1,6,6,16
%N A353645 a(1) = 1, and for n > 1, number of ways to write the square of n as a product of at least two factors, the largest two of which are equal.
%H A353645 Antti Karttunen, <a href="/A353645/b353645.txt">Table of n, a(n) for n = 1..16415</a>
%F A353645 a(n) = A325045(A000290(n)).
%e A353645 For n=6, 6^2 = 36 can be factorized in two ways so that two largest factors are equal, as 2*2*3*3 = 6*6, therefore a(6) = 2. See also the examples in A325045.
%o A353645 (PARI)
%o A353645 A325045(n, m=n, facs=List([])) = if(1==n, (0==#facs || (#facs>=2 && facs[1]==facs[2])), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs,d); s += A325045(n/d, d, newfacs))); (s));
%o A353645 A353645(n) = A325045(n^2);
%Y A353645 Cf. A000290, A325045.
%K A353645 nonn
%O A353645 1,4
%A A353645 _Antti Karttunen_, May 03 2022