A345663 Numbers k such that A001414(k) is divisible by A007953(k).

1, 2, 3, 4, 5, 7, 10, 27, 32, 42, 60, 70, 91, 100, 110, 114, 115, 124, 130, 132, 143, 154, 170, 182, 185, 188, 200, 204, 215, 220, 221, 222, 230, 232, 238, 242, 266, 276, 295, 308, 315, 326, 338, 342, 378, 402, 437, 450, 472, 485, 494, 532, 540, 555, 572, 576, 583, 588, 612, 620, 624, 636, 648

Offset: 1

Author

J. M. Bergot and Robert Israel, Jun 21 2021

Keywords

• nonn
• base

Examples

			a(10) = 42 is a term because A001414(42) =  2+3+7 = 12 is divisible by A007953(42) = 4+2 = 6.
		

Links

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

Crossrefs

Cf. A001414, A007953, A063737.

Programs

Maple

filter:= proc(n) local t;
  add(t[1]*t[2],t=ifactors(n)[2]) mod convert(convert(n,base,10),`+`) = 0
end proc:
select(filter, [$1..1000]);

Mathematica

Select[Range[650], Divisible[Plus @@ Times @@@ FactorInteger[#], Plus @@ IntegerDigits[#]] &] (* Amiram Eldar, Jun 21 2021 *)

PARI

sopfr(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1]*f[k,2]);
isok(k) = !(sopfr(k) % sumdigits(k)); \\ Michel Marcus, Jun 24 2021