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

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

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..18.

Example

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

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 *)

Prog

(Magma) [n: n in [2..1000000] | Denominator(SumOfDivisors(n) / (EulerPhi(n-1) + 1)) eq 1 ]
(PARI) lista(nn) = {for (n=2, nn, if (sigma(n) % (eulerphi(n-1)+1) == 0, print1(n, ", ")); ); } \\ Michel Marcus, Mar 29 2015

Crossrefs

Cf. A000010, A000203, A019434.

Sequence in context: A253204 A266165 A281622 * A256444 A032619 A193066

Adjacent sequences: A256436 A256437 A256438 * A256440 A256441 A256442

Keyword

nonn,more

Author

Jaroslav Krizek, Mar 29 2015

Extensions

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

Status

approved