A086455 Sum of divisors of prime powers: sigma(p^e).

1, 3, 4, 7, 6, 8, 15, 13, 12, 14, 31, 18, 20, 24, 31, 40, 30, 32, 63, 38, 42, 44, 48, 57, 54, 60, 62, 127, 68, 72, 74, 80, 121, 84, 90, 98, 102, 104, 108, 110, 114, 133, 156, 128, 255, 132, 138, 140, 150, 152, 158, 164, 168, 183, 174, 180, 182, 192, 194, 198

Offset: 1

Author

Reinhard Zumkeller, Jul 20 2003

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Divisor Function.
• Eric Weisstein's World of Mathematics, Prime Power.

Crossrefs

Cf. A000203, A000961, A025473, A025474, A086454.

Programs

Maple

A086455 := proc(n)
    numtheory[sigma](A000961(n)) ;
end proc: # R. J. Mathar, Jun 04 2016

Mathematica

DivisorSigma[1, #]& /@ Join[{1}, Select[Range[2, 200], PrimePowerQ]] (* Jean-François Alcover, Feb 10 2018 *)

PARI

list(lim) = apply(sigma, select(x -> x == 1 || isprimepower(x), vector(lim, i, i))); \\ Amiram Eldar, May 07 2025

Formula

a(n) = A000203(A000961(n)).

a(n) = (p^(e+1)-1)/(p-1), where p^e = A000961(n).

a(n) = (A025473(n)^(A025474(n)+1)-1)/(A025473(n)-1).