A256439 Numbers k such that phi(k-1)+1 divides sigma(k).

3, 5, 17, 26, 171, 257, 265, 1921, 9385, 26665, 65537, 263041, 437761, 1057801, 2038648321, 10866583226, 11453097097, 982923711145

Offset: 1

Author

Jaroslav Krizek, Mar 29 2015

Keywords

• nonn
• more

Comments

Numbers k such that A000010(k-1)+1 divides A000203(k).

Supersequence of Fermat primes (A019434).

Supersequence of A256444. Corresponding values of numbers k(n) = sigma(n) / (phi(n-1)+1) : 2, 2, 2, 2, 4, 2, 4, 4, 4, 4, 2, 4, 4, 4, ... - Jaroslav Krizek, Mar 31 2015

a(19) > 10^13. - Giovanni Resta, Jul 13 2015

Examples

			17 is in the sequence because phi(16) + 1 divides sigma(17); 9 divides 18.
		

Crossrefs

Cf. A000010, A000203, A019434.

Programs

Magma

[n: n in [2..1000000] | Denominator(SumOfDivisors(n) / (EulerPhi(n-1) + 1)) eq 1 ];

Maple

with(numtheory): A256439:=n->`if`(sigma(n) mod (phi(n-1)+1) = 0, n, NULL): seq(A256439(n), n=2..10^5); # Wesley Ivan Hurt, Mar 29 2015

Mathematica

Select[Range@ 1000000, Mod[DivisorSigma[1, #], EulerPhi[# - 1] + 1] == 0 &] (* Michael De Vlieger, Mar 29 2015 *)

PARI

lista(nn) = {for (n=2, nn, if (sigma(n) % (eulerphi(n-1)+1) == 0, print1(n, ", ")););} \\ Michel Marcus, Mar 29 2015

Extensions

a(15)-a(18) from Giovanni Resta, Jul 13 2015