A078317 Number of divisors of n*rad(n)+1, where rad = A007947 (squarefree kernel).

2, 2, 4, 3, 4, 2, 6, 2, 6, 2, 4, 2, 8, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 4, 12, 2, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 8, 6, 4, 2, 6, 4, 12, 8, 9, 4, 16, 3, 8, 4, 4, 8, 8, 6, 8, 4, 16, 4, 4, 2, 4, 4, 6, 4, 4, 2, 8, 6, 4, 6, 4, 2, 16, 2, 4, 8, 8, 4, 4, 6, 6, 6, 16, 2, 4, 4, 8, 4, 8, 4, 8, 8, 12, 2, 4, 2, 8, 2, 12, 8

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000005, A007947, A078310, A078313, A078314, A078318.

Programs

Haskell

a078317 = a000005 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

a[n_] := DivisorSigma[0, 1 + n * Times @@ FactorInteger[n][[;;, 1]]]; Array[a, 100] (* Amiram Eldar, Apr 10 2025 *)

PARI

a(n) = numdiv(1 + n * vecprod(factor(n)[, 1])); \\ Amiram Eldar, Apr 10 2025

Formula

a(n) = A000005(A078310(n)).