cp's OEIS Frontend

A341693 Numbers k whose sum of digits divides sigma(k)-k.

%I A341693 #51 Jun 04 2021 07:27:58
%S A341693 1,6,10,14,20,24,26,30,38,42,44,60,78,90,100,102,106,110,112,114,120,
%T A341693 121,132,150,153,176,182,190,198,202,204,210,220,222,224,240,244,258,
%U A341693 260,264,268,270,272,280,285,294,298,306,312,314,330,332,334,360,361,393,395
%N A341693 Numbers k whose sum of digits divides sigma(k)-k.
%e A341693 k=10 -> sigma(k)=1+2+5+10=18 sum_digits(k)=1+0=1 -> 18/1 = 18.
%e A341693 k=42 -> sigma(k)=1+2+3+6+7+14+21+42=96 sum_digits(k)=4+2=6 -> 96/6 = 16.
%p A341693 isA341693 := proc(n)
%p A341693     if modp(numtheory[sigma](n)-n,digsum(n)) =0 then
%p A341693         true;
%p A341693     else
%p A341693         false;
%p A341693     end if
%p A341693 end proc:
%p A341693 for n from 1 to 395 do
%p A341693     if isA341693(n) then
%p A341693         printf("%d,",n) ;
%p A341693     end if;
%p A341693 end do: # _R. J. Mathar_, Jun 04 2021
%t A341693 Select[Range[400], Divisible[DivisorSigma[1, #] - #, Plus @@ IntegerDigits[#]] &] (* _Amiram Eldar_, May 24 2021 *)
%o A341693 (PARI)
%o A341693 list(nn) = for(n=1, nn, if ((sigma(n)-n) % sumdigits(n) == 0, print1(n, ", ")))
%o A341693 list(1000)
%Y A341693 Cf. A007953, A001065, A132628.
%K A341693 nonn,base
%O A341693 1,2
%A A341693 _Zdenek Cervenka_, May 24 2021