A345663 - OEIS

%I #18 Jun 25 2021 01:51:41

%S 1,2,3,4,5,7,10,27,32,42,60,70,91,100,110,114,115,124,130,132,143,154,

%T 170,182,185,188,200,204,215,220,221,222,230,232,238,242,266,276,295,

%U 308,315,326,338,342,378,402,437,450,472,485,494,532,540,555,572,576,583,588,612,620,624,636,648

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

%H Robert Israel, <a href="/A345663/b345663.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p   add(t[1]*t[2],t=ifactors(n)[2]) mod convert(convert(n,base,10),`+`) = 0

%p end proc:

%p select(filter, [$1..1000]);

%t Select[Range[650], Divisible[Plus @@ Times @@@ FactorInteger[#], Plus @@ IntegerDigits[#]] &] (* _Amiram Eldar_, Jun 21 2021 *)

%o (PARI) sopfr(n) = my(f=factor(n)); sum(k=1, #f~, f[k,1]*f[k,2]);

%o isok(k) = !(sopfr(k) % sumdigits(k)); \\ _Michel Marcus_, Jun 24 2021

%Y Cf. A001414, A007953, A063737.

%K nonn,base

%O 1,2

%A _J. M. Bergot_ and _Robert Israel_, Jun 21 2021