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

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Maple

with(numtheory): seq(add(tau(d^2)*sigma(d), d in divisors(n)), n=1..60); # Ridouane Oudra, Aug 25 2019

Mathematica

a[n_] := DivisorSum[n, DivisorSigma[0, #^2] * DivisorSigma[1, #] &]; Array[a, 100] (* Amiram Eldar, Sep 15 2019 *)

Prog

(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

Crossrefs

Cf. A000203, A060648, A000005.

Sequence in context: A102249 A195313 A219829 * A069960 A219715 A154142

Adjacent sequences: A062367 A062368 A062369 * A062371 A062372 A062373

Keyword

nonn,mult

Author

Vladeta Jovovic, Jul 07 2001

Status

approved