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Numbers n such that sigma(n) == 0 (mod n+4).
3

%I #14 Sep 08 2022 08:46:17

%S 9,56,368,780,836,2352,11096,17816,45356,77744,91388,128768,254012,

%T 388076,430272,2087936,2291936,13174976,29465852,35021696,45335936,

%U 120888092,184773312,260378492,381236216,775397948,3381872252,4856970752,6800228816,8589344768,44257207676,114141404156,1461083549696,1471763808896,2199013818368

%N Numbers n such that sigma(n) == 0 (mod n+4).

%e sigma(9) mod 9+4 = 13 mod 13 = 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(10^9,4);

%t k = 4; Select[Range[Abs@ k + 1, 10^6], Mod[DivisorSigma[1, #], # + k] == 0 &] (* _Michael De Vlieger_, Jul 01 2016 *)

%o (Magma) [n: n in [1..2*10^6] | SumOfDivisors(n) mod (n+4) eq 0 ]; // _Vincenzo Librandi_, Jul 02 2016

%Y Cf. A045770, A067702, A088833, A181598, A274551, A274552, A274554-A274566.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Jun 28 2016

%E a(18)-a(35) from _Giovanni Resta_