cp's OEIS Frontend

A062370 a(n) = Sum_{i|n,j|n} sigma(i)*sigma(j)/sigma(gcd(i,j)), where sigma(n) = sum of divisors of n.

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