A292770 If sigma(n)+phi(n) is even then a(n) = (sigma(n)+phi(n))/2 otherwise -1.

1, 2, 3, -1, 5, 7, 7, -1, -1, 11, 11, 16, 13, 15, 16, -1, 17, -1, 19, 25, 22, 23, 23, 34, -1, 27, 29, 34, 29, 40, 31, -1, 34, 35, 36, -1, 37, 39, 40, 53, 41, 54, 43, 52, 51, 47, 47, 70, -1, -1, 52, 61, 53, 69, 56, 72, 58, 59, 59, 92, 61, 63, 70, -1, 66, 82, 67, 79, 70, 84, 71, -1, 73, 75, 82, 88, 78, 96

Offset: 1

Author

N. J. A. Sloane, Sep 28 2017

Keywords

• sign
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A028982, A065387, A291790, A292108, A292766, A292771.

Programs

Maple

f:= proc(n) local v;
   v:= numtheory:-sigma(n)+numtheory:-phi(n);
   if v::even then v/2 else -1 fi
end proc:
map(f, [$1..100]); # Robert Israel, Sep 28 2017

Mathematica

Table[If[EvenQ[DivisorSigma[1,n]+EulerPhi[n]],(DivisorSigma[1,n]+EulerPhi[n])/2,-1],{n,120}] (* Harvey P. Dale, Jun 19 2022 *)

PARI

a(n) = {my(f = factor(n), s = sigma(f) + eulerphi(f)); if(s%2, -1, s/2);} \\ Amiram Eldar, Dec 06 2024

Formula

a(n) = -1 if and only if n is in A028982 \ {1, 2}. - Amiram Eldar, Dec 06 2024