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%I #15 Nov 07 2024 03:49:18
%S 1,4,7,10,15,18,21,24,29,36,39,42,47,50,53,56,65,68,75,78,83,86,89,92,
%T 97,108,111,118,123,126,129,132,141,144,147,150,163,166,169,172,177,
%U 180,183,186,191,198,201,204,213,228,239,242,247,250,257,260,265,268
%N Number of 2 X 2 symmetric singular matrices with entries from {0,...,n}.
%H Vaclav Kotesovec, <a href="/A064368/b064368.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = n + 1 + 2*Sum_{k=1..n} Sum_{d^2|k} phi(d), where phi = Euler totient function A000010.
%F a(n) ~ (n/zeta(2)) * (log(n) + 3*gamma - 1 + zeta(2) - 2*zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Nov 07 2024
%t f[p_, e_] := p^Floor[e/2]; a[0] = 0; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; With[{max = 100}, 1 + Range[0, max] + 2 * Accumulate[Array[a, max + 1, 0]]] (* _Amiram Eldar_, Nov 07 2024 *)
%o (PARI) a(n) = n + 1 + 2*sum(k=1, n, sumdiv(k, d, issquare(d)*eulerphi(sqrtint(d)))) \\ _Michel Marcus_, Jun 17 2013
%Y Cf. A000010, A000188, A064276, A059306, A062801, A059976, A039623.
%Y Cf. A001620, A306016.
%K nonn
%O 0,2
%A _Vladeta Jovovic_, Sep 27 2001