A341321 - OEIS

%I #12 Nov 08 2023 12:35:08

%S 4,6,8,9,10,12,14,15,16,22,26,27,30,34,38,46,58,60,62,64,70,72,74,82,

%T 84,86,94,105,106,118,122,126,128,134,140,142,144,146,150,158,166,168,

%U 178,180,194,202,206,214,218,220,226,231,240,254,256,262,264,270,274,278,280,286,288,298,302,308

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

%H Robert Israel, <a href="/A341321/b341321.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p filter:= proc(n) local s,m,t;

%p    if isprime(n) then return false fi;

%p    s:= add(t[1]*t[2],t=ifactors(n)[2]);

%p    m:= n mod s;

%p    n mod (m+s) = 0

%p end proc:

%p select(filter, [$4..10000]);

%t sopfr[n_] := Total[Times @@@ FactorInteger[n]];

%t okQ[n_] := CompositeQ[n] && With[{s = sopfr[n]}, Divisible[n, Mod[n, s]+s]];

%t Select[Range[4, 1000], okQ] (* _Jean-François Alcover_, Nov 08 2023 *)

%Y Includes A100484.

%Y Cf. A001414.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 08 2021