A078321 Euler's totient of n*rad(n)+1, where rad = A007947 (squarefree kernel).

1, 4, 4, 6, 12, 36, 20, 16, 12, 100, 60, 72, 64, 196, 112, 20, 112, 108, 180, 132, 192, 384, 208, 112, 36, 676, 40, 260, 420, 832, 432, 48, 432, 1056, 612, 180, 544, 1088, 760, 400, 812, 1408, 720, 576, 312, 2016, 768, 272, 168, 332, 1300, 800, 1120, 240

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A007947, A078310.

Programs

Haskell

a078321 = a000010 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

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

PARI

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

Formula

a(n) = A000010(A078310(n)).