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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001414, A007953, A063737.

Sequence in context: A212463 A130080 A057496 * A191864 A180348 A001729

Adjacent sequences: A345660 A345661 A345662 * A345664 A345665 A345666

Keyword

nonn,base

Author

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

Status

approved