A274551 - OEIS

%I #37 Sep 08 2022 08:46:17

%S 4,8925,32445,442365

%N Numbers k such that sigma(k) == 0 (mod k+3).

%C a(5) > 10^8 if it exists. - _Felix Fröhlich_, Jul 01 2016

%C No more terms < 6.5*10^14. - _Jud McCranie_, Dec 02 2019

%e sigma(4) mod (4+3) = 7 mod 7 = 0.

%p with(numtheory); P:=proc(q,h) local n;  for n from 1 to q do

%p if n+h>0 then if type(sigma(n)/(n+h),integer) then print(n); fi; fi; od; end: P(10^9,3);

%t Select[Range[10^6], Mod[DivisorSigma[1, #], # + 3] == 0 &] (* _Michael De Vlieger_, Jul 01 2016 *)

%o (PARI) is(n) = Mod(sigma(n), n+3)==0 \\ _Felix Fröhlich_, Jul 01 2016

%o (Magma) [n: n in [1..2*10^6] | SumOfDivisors(n) mod (n+3) eq 0 ]; // _Vincenzo Librandi_, Jul 02 2016

%Y Cf. A000203, A067702, A087167, A088834, A274552, A274553, A274554, A274556.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Jun 28 2016