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
KEYWORD
nonn,mult
AUTHOR
Vladeta Jovovic, Jul 07 2001
STATUS
approved