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%I #24 Sep 08 2022 08:46:11
%S 3,5,17,26,171,257,265,1921,9385,26665,65537,263041,437761,1057801,
%T 2038648321,10866583226,11453097097,982923711145
%N Numbers n such that phi(n-1)+1 divides sigma(n).
%C Numbers n such that A000010(n-1)+1 divides A000203(n).
%C Supersequence of Fermat primes (A019434).
%C 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
%C a(19) > 10^13. - _Giovanni Resta_, Jul 13 2015
%e 17 is in the sequence because phi(16) + 1 divides sigma(17); 9 divides 18.
%p 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
%t Select[Range@ 1000000, Mod[DivisorSigma[1, #], EulerPhi[# - 1] + 1] == 0 &] (* _Michael De Vlieger_, Mar 29 2015 *)
%o (Magma) [n: n in [2..1000000] | Denominator(SumOfDivisors(n) / (EulerPhi(n-1) + 1)) eq 1 ]
%o (PARI) lista(nn) = {for (n=2, nn, if (sigma(n) % (eulerphi(n-1)+1) == 0, print1(n, ", ")););} \\ _Michel Marcus_, Mar 29 2015
%Y Cf. A000010, A000203, A019434.
%K nonn,more
%O 1,1
%A _Jaroslav Krizek_, Mar 29 2015
%E a(15)-a(18) from _Giovanni Resta_, Jul 13 2015
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