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

1,1

Links

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

Formula

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

Mathematica

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

Prog

(Haskell)
a078317 = a000005 . a078310  -- Reinhard Zumkeller, Jul 23 2013
(PARI) a(n) = numdiv(1 + n * vecprod(factor(n)[, 1])); \\ Amiram Eldar, Apr 10 2025

Crossrefs

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

Sequence in context: A051297 A371409 A338756 * A382872 A105016 A377369

Adjacent sequences: A078314 A078315 A078316 * A078318 A078319 A078320

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 23 2002

Status

approved