cp's OEIS Frontend

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

%I A298563 #39 May 28 2025 01:10:03
%S A298563 1,3,5,6,14,44,110,152,884,2144,8384,18632,116624,8394752,15370304,
%T A298563 73995392,536920064,2147581952,34360131584,27034175140420610,
%U A298563 36028797421617152,576460753914036224
%N A298563 Numbers k such that k - 2 | sigma(k).
%C A298563 Similar to A055708.
%C A298563 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 A298563 Superset of A125246. - _Giovanni Resta_, Jan 23 2018
%C A298563 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
%e A298563 For k=44, sigma(k)/(k-2) = sigma(44)/(44-2) = 84/42 = 2, so 44 belongs to the sequence;
%e A298563 for k=110, sigma(k)/(k-2) = sigma(110)/(110-2) = 216/108 = 2, so 110 is also a term.
%t A298563 Select[Range[10^6], Divisible[DivisorSigma[1, #], # - 2] &] (* _Michael De Vlieger_, Jan 21 2018 *)
%o A298563 (PARI) isok(k) = (k!=2) && !(sigma(k) % (k-2)); \\ _Michel Marcus_, Jan 22 2018
%o A298563 (Magma) [n: n in [3..10^7]| DivisorSigma(1, n) mod (n-2) eq 0]; // _Vincenzo Librandi_, Jan 22 2018
%Y A298563 Cf. A055708, A057732, A125246.
%K A298563 nonn,more
%O A298563 1,2
%A A298563 _Zdenek Cervenka_, Jan 21 2018
%E A298563 a(17)-a(18) from _Robert G. Wilson v_, Jan 21 2018
%E A298563 a(19) from _Giovanni Resta_, Jan 23 2018
%E A298563 a(20)-a(22) from _Max Alekseyev_, May 27 2025