A164114 Numbers k such that Chowla(k) + phi(k) is prime.

3, 6, 10, 12, 20, 22, 24, 44, 46, 54, 58, 66, 68, 70, 78, 80, 82, 84, 88, 90, 106, 116, 120, 136, 138, 154, 156, 160, 166, 168, 174, 178, 184, 186, 188, 190, 192, 212, 226, 234, 246, 250, 252, 258, 262, 270, 284, 286, 300, 306, 318, 320, 328, 330, 332, 336, 346, 352, 356

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 10 2009

Keywords

• nonn

Comments

Indices such that the sum of the nontrivial divisors and of the Euler totient function at that index is prime.

Examples

			n=3 is in the sequence because Chowla(3) + phi(3) = 0 + 2 = 2 (a prime);
n=6 is in the sequence because Chowla(6) + phi(5) = 5 + 2 = 7 (a prime).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000010, A000040, A000203, A048050.

Programs

Magma

[n: n in [1..400] | IsPrime((SumOfDivisors(n)+EulerPhi(n))-n-1)]; // Vincenzo Librandi, Sep 12 2017

Maple

A048050 := proc(n) if n = 1 then 0; else numtheory[sigma](n)-n-1 ; fi; end:
A000010 := proc(n) numtheory[phi](n) ; end: isA164114 := proc(n) isprime( A000010(n)+A048050(n)) ; end:
for n from 1 to 400 do if isA164114(n) then printf("%d,",n): fi; od: # R. J. Mathar, Aug 27 2009

Mathematica

f[n_] := Plus @@ Divisors[n] - n - 1; Select[Range[100], PrimeQ[f[#] + EulerPhi[#]] &] (* G. C. Greubel, Sep 11 2017 *)

PARI

isok(n) = isprime(sigma(n)+eulerphi(n)-n-1); \\ Michel Marcus, Sep 12 2017

Formula

{k: A048050(k)+A000010(k) in A000040}.

Extensions

34 and 60 removed, 54 inserted by R. J. Mathar, Aug 27 2009