OFFSET
1,2
COMMENTS
If p is prime, a(p) = Sum_{d|p} d * sigma_d(d) = 1*(1^1) + p*(1^p + p^p) = 1 + p + p^(p+1).
EXAMPLE
a(6) = Sum_{d|6} d * sigma_d(d) = 1*(1^1) + 2*(1^2 + 2^2) + 3*(1^3 + 3^3) + 6*(1^6 + 2^6 + 3^6 + 6^6) = 284795.
MATHEMATICA
Table[Sum[k*DivisorSigma[k, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 30}]
PROG
(PARI) a(n) = sumdiv(n, d, d*sigma(d, d)); \\ Michel Marcus, May 21 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 20 2021
STATUS
approved