A078318 Sum of divisors of n*rad(n)+1, where rad = A007947 (squarefree kernel).

3, 6, 18, 13, 42, 38, 93, 18, 56, 102, 186, 74, 324, 198, 342, 48, 540, 110, 546, 272, 756, 588, 972, 180, 312, 678, 126, 528, 1266, 972, 1596, 84, 1980, 1260, 1842, 256, 2484, 1842, 2286, 402, 2613, 2124, 3534, 1440, 1281, 2220, 4536, 307, 660, 672

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A007947, A078310, A078317, A078319, A078320.

Programs

Haskell

a078318 = a000203 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

a[n_] := DivisorSigma[1, 1 + n * Times @@ FactorInteger[n][[;;, 1]]]; Array[a, 100] (* Amiram Eldar, Apr 10 2025 *)

PARI

rad(n)=vecprod(factor(n)[,1])
a(n)=sigma(n*rad(n)+1) \\ Charles R Greathouse IV, Jul 09 2013

Formula

a(n) = A000203(A078310(n)).