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%I #12 Sep 14 2023 02:31:06
%S 1,7,7,17,7,49,7,31,17,49,7,119,7,49,49,49,7,119,7,119,49,49,7,217,17,
%T 49,31,119,7,343,7,71,49,49,49,289,7,49,49,217,7,343,7,119,119,49,7,
%U 343,17,119,49,119,7,217,49,217,49,49,7,833,7,49,119
%N Number of 2 X 2 matrices with elements in {1,2,...,n} such that LCMs of rows and columns are n.
%H Antti Karttunen, <a href="/A100635/b100635.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = 2*((e+1)^2) - 1.
%F Dirichlet g.f.: zeta(s)^3 * Product_{p prime} (1 + 4/p^s - 1/p^(2*s)). - _Amiram Eldar_, Sep 14 2023
%t Flatten[{1, Table[Product[2*((e+1)^2) - 1, {e, FactorInteger[n][[All, 2]]}], {n, 2, 100}]}] (* _Vaclav Kotesovec_, Sep 20 2020 *)
%o (PARI) A100635(n) = { my(f = factor(n), m = 1); for (k=1, #f~, m *= (2*((f[k, 2]+1)^2))-1; ); m; } \\ _Antti Karttunen_, May 25 2017
%Y Cf. A048691.
%K mult,easy,nonn
%O 1,2
%A _Vladeta Jovovic_, Dec 03 2004
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