A039649 a(n) = phi(n)+1.

2, 2, 3, 3, 5, 3, 7, 5, 7, 5, 11, 5, 13, 7, 9, 9, 17, 7, 19, 9, 13, 11, 23, 9, 21, 13, 19, 13, 29, 9, 31, 17, 21, 17, 25, 13, 37, 19, 25, 17, 41, 13, 43, 21, 25, 23, 47, 17, 43, 21, 33, 25, 53, 19, 41, 25, 37, 29, 59, 17, 61, 31, 37, 33, 49, 21, 67, 33, 45, 25, 71, 25, 73, 37, 41

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• easy

Comments

a(p) = p for p prime.

Records give A000040. - Omar E. Pol, Jul 10 2014

Which n are divisible by phi(n)+1? See A085118 for a possible answer and references. - Peter Munn, Jun 03 2021

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Crossrefs

Cf. A000010, A039650, A039651, A039652, A039653, A039654, A039655, A039656, A085118.

Programs

Haskell

a039649 = (+ 1) . a000010  -- Reinhard Zumkeller, Oct 07 2015

Magma

[EulerPhi(n)+1: n in [1..100]]; // Vincenzo Librandi, Aug 13 2013

Mathematica

Table[EulerPhi[n] + 1, {n, 100}] (* Vincenzo Librandi, Aug 13 2013 *)

PARI

a(n)=eulerphi(n)+1 \\ Charles R Greathouse IV, Mar 04 2017

Formula

a(n) = A000010(n) + 1.

a(n) <= n for n > 1.

G.f.: x/(1 - x) + Sum_{k>=1} mu(k)*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Mar 16 2017

Extensions

Edited by Charles R Greathouse IV, Mar 18 2010.