A069915 Sum of (1+phi)-divisors of n (cf. A061389).

1, 3, 4, 3, 6, 12, 8, 7, 4, 18, 12, 12, 14, 24, 24, 11, 18, 12, 20, 18, 32, 36, 24, 28, 6, 42, 13, 24, 30, 72, 32, 31, 48, 54, 48, 12, 38, 60, 56, 42, 42, 96, 44, 36, 24, 72, 48, 44, 8, 18, 72, 42, 54, 39, 72, 56, 80, 90, 60, 72, 62, 96, 32, 35, 84, 144, 68, 54, 96, 144, 72

Offset: 1

Author

Vladeta Jovovic, Apr 23 2002

Keywords

• mult
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061389.

Cf. A027748, A124010, A038566, A051378.

Programs

Haskell

a069915 n = product $ zipWith sum_1phi (a027748_row n) (a124010_row n)
   where sum_1phi p e = 1 + sum [p ^ k | k <- a038566_row e]
-- Reinhard Zumkeller, Mar 13 2012

Mathematica

a[1] = 1; a[p_?PrimeQ] = p + 1; a[n_] := Times @@ (1 + Sum[If[GCD[k, Last[#]] == 1, First[#]^k, 0], {k, 1, Last[#]}] & ) /@ FactorInteger[n]; Table[a[n], {n, 1, 71}] (* Jean-François Alcover, May 04 2012 *)

PARI

a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(k = 1, f[i, 2], (gcd(k, f[i, 2]) == 1) * f[i, 1]^k));} \\ Amiram Eldar, Aug 15 2023

Formula

Multiplicative with a(p^e) = 1+Sum_{k=1..e, gcd(k, e)=1} p^k.