A341321 Composite numbers k that are divisible by (k mod sopfr(k))+sopfr(k), where sopfr = A001414.

4, 6, 8, 9, 10, 12, 14, 15, 16, 22, 26, 27, 30, 34, 38, 46, 58, 60, 62, 64, 70, 72, 74, 82, 84, 86, 94, 105, 106, 118, 122, 126, 128, 134, 140, 142, 144, 146, 150, 158, 166, 168, 178, 180, 194, 202, 206, 214, 218, 220, 226, 231, 240, 254, 256, 262, 264, 270, 274, 278, 280, 286, 288, 298, 302, 308

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 8 is a term because 8 is composite, sopfr(8) = 3*2 = 6, 8 mod 6 = 2, and 8 is divisible by 2+6.

Maple

filter:= proc(n) local s, m, t;
   if isprime(n) then return false fi;
   s:= add(t[1]*t[2], t=ifactors(n)[2]);
   m:= n mod s;
   n mod (m+s) = 0
end proc:
select(filter, [$4..10000]);

Mathematica

sopfr[n_] := Total[Times @@@ FactorInteger[n]];
okQ[n_] := CompositeQ[n] && With[{s = sopfr[n]}, Divisible[n, Mod[n, s]+s]];
Select[Range[4, 1000], okQ] (* Jean-François Alcover, Nov 08 2023 *)

Crossrefs

Includes A100484.

Cf. A001414.

Sequence in context: A117098 A077136 A098216 * A063806 A323521 A063989

Adjacent sequences: A341318 A341319 A341320 * A341322 A341323 A341324

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Feb 08 2021

Status

approved