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%I #20 Sep 15 2019 13:50:15
%S 1,10,13,45,19,130,25,150,78,190,37,585,43,250,247,429,55,780,61,855,
%T 325,370,73,1950,174,430,358,1125,91,2470,97,1122,481,550,475,3510,
%U 115,610,559,2850,127,3250,133,1665,1482,730,145,5577,310,1740,715,1935
%N a(n) = Sum_{i|n,j|n} sigma(i)*sigma(j)/sigma(gcd(i,j)), where sigma(n) = sum of divisors of n.
%H Amiram Eldar, <a href="/A062370/b062370.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = 1 + Sum_{k=1..e} (2k+1)sigma(p^k). - _Mitch Harris_, May 24 2005
%F a(n) = Sum_{d|n} tau(d^2)*sigma(d), where tau(k) = A000005(k) and sigma(k) = A000203(k). - _Ridouane Oudra_, Aug 25 2019
%p with(numtheory): seq(add(tau(d^2)*sigma(d), d in divisors(n)), n=1..60); # _Ridouane Oudra_, Aug 25 2019
%t a[n_] := DivisorSum[n, DivisorSigma[0, #^2] * DivisorSigma[1, #] &]; Array[a, 100] (* _Amiram Eldar_, Sep 15 2019 *)
%o (PARI) a(n) = my(f=factor(n)); for (j=1, #f~, f[j,1] = 1+ sum(k=1, f[j,2], (2*k+1)*sigma(f[j,1]^k)); f[j,2] = 1); factorback(f); \\ _Michel Marcus_, Feb 28 2019
%Y Cf. A000203, A060648, A000005.
%K nonn,mult
%O 1,2
%A _Vladeta Jovovic_, Jul 07 2001
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