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A274566 Numbers n such that sigma(n)==0 (mod n-10). 12
11, 12, 14, 22, 40, 42, 46, 154, 190, 2656, 6490, 44650, 318250, 1360810, 1503370, 1788490, 3214090, 103712410, 3915380170, 6077111050, 9796360330, 10828121356, 33086522327050, 35966517350410 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

sigma(11) mod (11 - 10) = 12 mod 1 = 0.

MAPLE

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

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

MATHEMATICA

k=-10; Select[Range[Abs@k+1, 10^7], Mod[DivisorSigma[1, #], #+k] == 0 &] (* Vincenzo Librandi, Jul 06 2016 *)

PROG

(MAGMA) [n: n in [11..2*10^6] | SumOfDivisors(n) mod (n-10) eq 0 ]; // Vincenzo Librandi, Jul 06 2016

CROSSREFS

Cf. A045770, A067702, A088833, A181598, A223607, A274551-A274565.

Sequence in context: A034907 A045987 A121978 * A213309 A128997 A189836

Adjacent sequences:  A274563 A274564 A274565 * A274567 A274568 A274569

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jul 06 2016

EXTENSIONS

a(17)-a(22) from Giovanni Resta, Jul 06 2016

a(23)-a(24) from Jud McCranie, Dec 2 2019

STATUS

approved

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Last modified November 26 07:49 EST 2020. Contains 338632 sequences. (Running on oeis4.)