A298563 Numbers k such that k - 2 | sigma(k).

1, 3, 5, 6, 14, 44, 110, 152, 884, 2144, 8384, 18632, 116624, 8394752, 15370304, 73995392, 536920064, 2147581952, 34360131584, 27034175140420610, 36028797421617152, 576460753914036224

Offset: 1

Author

Zdenek Cervenka, Jan 21 2018

Keywords

• nonn
• more

Comments

Similar to A055708.

Sequence includes every number of the form 2^(j-1)*(2^j+3) such that 2^j+3 is prime (i.e., j is a term in A057732); terms of this form are 5, 14, 44, 152, 2144, 8384, 8394752, 536920064, 2147581952, 34360131584, ... - Jon E. Schoenfield, Jan 22 2018

Superset of A125246. - Giovanni Resta, Jan 23 2018

Contains 2 times odd terms of A191363. Also, if m is a term of A056006 and q := (sigma(m) + 2)/m is coprime to m, them q*m is a term. - Max Alekseyev, May 25 2025

Examples

			For k=44, sigma(k)/(k-2) = sigma(44)/(44-2) = 84/42 = 2, so 44 belongs to the sequence;
for k=110, sigma(k)/(k-2) = sigma(110)/(110-2) = 216/108 = 2, so 110 is also a term.
		

Crossrefs

Cf. A055708, A057732, A125246.

Programs

Magma

[n: n in [3..10^7]| DivisorSigma(1, n) mod (n-2) eq 0]; // Vincenzo Librandi, Jan 22 2018

Mathematica

Select[Range[10^6], Divisible[DivisorSigma[1, #], # - 2] &] (* Michael De Vlieger, Jan 21 2018 *)

PARI

isok(k) = (k!=2) && !(sigma(k) % (k-2)); \\ Michel Marcus, Jan 22 2018

Extensions

a(17)-a(18) from Robert G. Wilson v, Jan 21 2018

a(19) from Giovanni Resta, Jan 23 2018

a(20)-a(22) from Max Alekseyev, May 27 2025