A062370 a(n) = Sum_{i|n,j|n} sigma(i)*sigma(j)/sigma(gcd(i,j)), where sigma(n) = sum of divisors of n.
1, 10, 13, 45, 19, 130, 25, 150, 78, 190, 37, 585, 43, 250, 247, 429, 55, 780, 61, 855, 325, 370, 73, 1950, 174, 430, 358, 1125, 91, 2470, 97, 1122, 481, 550, 475, 3510, 115, 610, 559, 2850, 127, 3250, 133, 1665, 1482, 730, 145, 5577, 310, 1740, 715, 1935
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Maple
with(numtheory): seq(add(tau(d^2)*sigma(d), d in divisors(n)), n=1..60); # Ridouane Oudra, Aug 25 2019
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Mathematica
a[n_] := DivisorSum[n, DivisorSigma[0, #^2] * DivisorSigma[1, #] &]; Array[a, 100] (* Amiram Eldar, Sep 15 2019 *)
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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
Formula
Multiplicative with a(p^e) = 1 + Sum_{k=1..e} (2k+1)sigma(p^k). - Mitch Harris, May 24 2005
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