OFFSET
1,1
COMMENTS
If n is prime, then a(n) = (n + 1)*(2n + 3). - Wesley Ivan Hurt, May 14 2021
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = Sum_{d|n} (d + 2*sigma(d^2)*(n/d)). - Wesley Ivan Hurt, Jun 22 2025
a(p^k) = (p^(k+1)-1)*(2*p^(k+1)+p-3)/(p-1)^2 for p prime, k>=1. - Wesley Ivan Hurt, Jul 02 2025
MAPLE
A227241 := proc(n)
numtheory[sigma](n) ;
%*(2*%+1) ;
end proc:
seq(A227241(n), n=1..80) ; # R. J. Mathar, Jul 07 2013
MATHEMATICA
Table[DivisorSigma[1, n]*(2*DivisorSigma[1, n] + 1), {n, 1, 50}] (* G. C. Greubel, Oct 01 2017 *)
#(2#+1)&/@DivisorSigma[1, Range[50]] (* Harvey P. Dale, Aug 20 2024 *)
PROG
(PARI) for(n=1, 50, print1(sigma(n)*(2*sigma(n) + 1), ", ")) \\ G. C. Greubel, Oct 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jul 03 2013
STATUS
approved