A132628 -id:A132628 - cp's OEIS frontend

A132629 Sigma(n)/Sum_digits(n) for n such that sigma(n) is divisible by Sum_digits(n).

1, 2, 18, 6, 4, 2, 21, 9, 10, 24, 8, 8, 6, 16, 12, 14, 28, 12, 12, 9, 9, 5, 8, 26, 217, 51, 72, 26, 42, 32, 11, 108, 62, 40, 18, 120, 28, 32, 63, 56, 27, 24, 32, 21, 18, 19, 62, 26, 54, 24, 24, 12, 32, 30, 16, 36, 21, 26

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Aug 24 2007

			n=147 -> sigma(n)=1+3+7+21+49+147=228 Sum_digits(n)=1+4+7=12 -> 228/12 = 19
n=177 -> sigma(n)=1+3+59+177=240 Sum_digits(n)=1+7+7=15 -> 240/15 = 16

Cf. A007691, A054030, A132628.

with(numtheory); P:=proc(n) local a,i,j,k,w; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; j:=sigma(i)/w; if trunc(j)=j then print(j); fi; od; end: P(200);

Select[Table[DivisorSigma[1,n]/Total[IntegerDigits[n]],{n,300}], IntegerQ] (* Harvey P. Dale, Oct 01 2015 *)

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

Original entry on oeis.org

1, 6, 10, 14, 20, 24, 26, 30, 38, 42, 44, 60, 78, 90, 100, 102, 106, 110, 112, 114, 120, 121, 132, 150, 153, 176, 182, 190, 198, 202, 204, 210, 220, 222, 224, 240, 244, 258, 260, 264, 268, 270, 272, 280, 285, 294, 298, 306, 312, 314, 330, 332, 334, 360, 361, 393, 395

Offset: 1

Zdenek Cervenka, May 24 2021

			k=10 -> sigma(k)=1+2+5+10=18 sum_digits(k)=1+0=1 -> 18/1 = 18.
k=42 -> sigma(k)=1+2+3+6+7+14+21+42=96 sum_digits(k)=4+2=6 -> 96/6 = 16.

Cf. A007953, A001065, A132628.

isA341693 := proc(n)
    if modp(numtheory[sigma](n)-n,digsum(n)) =0 then
        true;
    else
        false;
    end if
end proc:
for n from 1 to 395 do
    if isA341693(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jun 04 2021

Select[Range[400], Divisible[DivisorSigma[1, #] - #, Plus @@ IntegerDigits[#]] &] (* Amiram Eldar, May 24 2021 *)

list(nn) = for(n=1, nn, if ((sigma(n)-n) % sumdigits(n) == 0, print1(n, ", ")))
list(1000)

cp's OEIS Frontend

A132629 Sigma(n)/Sum_digits(n) for n such that sigma(n) is divisible by Sum_digits(n).

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