A038344 Numbers k such that phi(k) + sigma(k) is a prime.

1, 8, 9, 32, 36, 50, 100, 225, 242, 484, 512, 578, 729, 800, 900, 1089, 1156, 1250, 1936, 2025, 2048, 2304, 2312, 2601, 2916, 3025, 3872, 4418, 6400, 7225, 7744, 8192, 8464, 8836, 9216, 10000, 12800, 14400, 20000, 20736, 21609, 26896, 27556, 31684, 32768, 33856, 34322

Offset: 1

Author

Felice Russo

Keywords

• nonn

Comments

Indices k such that A065387(k) is a prime number. - R. J. Mathar, Aug 26 2009

All terms are squares or twice squares (A028982). - Donovan Johnson, Sep 27 2013

Examples

			a(2) = 8 because phi(8) + sigma(8) = 19.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A000027, A000040, A000203, A028982.

Programs

Magma

[n: n in [1..40000] | IsPrime(EulerPhi(n)+DivisorSigma(1,n))]; // Vincenzo Librandi, Jul 22 2016

Mathematica

Select[Range[0, 40000], PrimeQ[DivisorSigma[1, #] + EulerPhi[#]] &] (* Vincenzo Librandi, Jul 22 2016 *)

PARI

isok(n) = isprime(eulerphi(n) + sigma(n)); \\ Michel Marcus, Sep 27 2013

PARI

v=vector(1000); c=0; for(j=1, 12105, m=j^2; if(isprime(eulerphi(m)+sigma(m)), c++; v[c]=m)); for(j=1, 8559, m=2*j^2; if(isprime(eulerphi(m)+sigma(m)), c++; v[c]=m)); v=vecsort(v); for(n=1, 1000, write("b038344.txt", n " " v[n])) \\ Donovan Johnson, Sep 27 2013

Formula

{k: A000203(k) + A000010(k) in A000040}. - R. J. Mathar, Aug 26 2009

Extensions

More terms from Olivier Gérard