A036924 Digit sum of composite even number equals digit sum of juxtaposition of its prime factors (counted with multiplicity).

4, 22, 58, 94, 166, 202, 274, 346, 378, 382, 438, 454, 526, 562, 576, 588, 634, 636, 648, 654, 666, 690, 706, 728, 762, 778, 852, 922, 958, 1086, 1282, 1284, 1376, 1626, 1642, 1678, 1736, 1776, 1822, 1842, 1858, 1872, 1894, 1908, 1952, 1962, 1966, 2038

Offset: 1

Author

Patrick De Geest, Jan 04 1999

Keywords

• nonn
• base

Comments

Even Smith numbers. - Robert Israel, Aug 24 2024

Links

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

Crossrefs

Cf. A006753, A019506, A036925.

Programs

Maple

filter:= proc(n) local F;
  F:= ifactors(n)[2];
  convert(convert(n,base,10),`+`) = convert(map(t -> t[2]*convert(convert(t[1],base,10),`+`), F),`+`)
end proc:
select(filter, [seq(i,i=4..10000,2)]); # Robert Israel, Aug 24 2024

Mathematica

d[n_] := IntegerDigits[n]; co[n_,k_] := Nest[Flatten[d[{#,n}]]&, n, k-1]; t={}; Do[If[!PrimeQ[n] && Total[d[n]] == Total[Flatten[d[co@@@FactorInteger[n]]]], AppendTo[t,n]], {n,4,2040,2}]; t (* Jayanta Basu, Jun 04 2013 *)

Extensions

Title made more precise by Sean A. Irvine, Nov 30 2020