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%I #35 Sep 08 2022 08:46:20
%S 1,3,5,6,14,44,110,152,884,2144,8384,18632,116624,8394752,15370304,
%T 73995392,536920064,2147581952,34360131584
%N Numbers k such that k - 2 | sigma(k).
%C Similar to A055708.
%C 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
%C Superset of A125246. a(20) > 10^12. - _Giovanni Resta_, Jan 23 2018
%e For k=44, sigma(k)/(k-2) = sigma(44)/(44-2) = 84/42 = 2, so 44 belongs to the sequence;
%e for k=110, sigma(k)/(k-2) = sigma(110)/(110-2) = 216/108 = 2, so 110 is also a term.
%t Select[Range[10^6], Divisible[DivisorSigma[1, #], # - 2] &] (* _Michael De Vlieger_, Jan 21 2018 *)
%o (PARI) isok(k) = (k!=2) && !(sigma(k) % (k-2)); \\ _Michel Marcus_, Jan 22 2018
%o (Magma) [n: n in [3..10^7]| DivisorSigma(1, n) mod (n-2) eq 0]; // _Vincenzo Librandi_, Jan 22 2018
%Y Cf. A055708, A057732, A125246.
%K nonn,more
%O 1,2
%A _Zdenek Cervenka_, Jan 21 2018
%E a(17)-a(18) from _Robert G. Wilson v_, Jan 21 2018
%E a(19) from _Giovanni Resta_, Jan 23 2018
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