A038367 Numbers n with property that (product of digits of n) is divisible by (sum of digits of n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 22, 30, 36, 40, 44, 50, 60, 63, 66, 70, 80, 88, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 120, 123, 130, 132, 138, 140, 145, 150, 154, 159, 160, 167, 170, 176, 180, 183, 189, 190, 195, 198, 200, 201, 202, 203

Offset: 1

Author

Felice Russo

Keywords

• nonn
• base
• easy

Comments

Equal to the disjoint union of A061013 and A011540 \ {0}. Contains in particular all positive single-digit integers, those with a digit 0, and 22*{1,...,18}. If x is in the sequence, any digit-permutation of x is also in the sequence. - M. F. Hasler, Feb 28 2018

Links

• Iain Fox, Table of n, a(n) for n = 1..10000

Crossrefs

See A061013 for case where 0 digits are excluded. Cf. A055931.

Programs

Magma

[0] cat [n: n in [1..250] | IsIntegral(&*Intseq(n)/&+Intseq(n))]; // Bruno Berselli, Feb 09 2016

Maple

isA038367 := proc(n)
    if type( A007954(n)/A007953(n),'integer') then
        true;
     else
        false;
    end if;
end proc :
for n from 1 to 500 do
    if isA038367(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jun 30 2020

Mathematica

okQ[n_]:=Module[{idn=IntegerDigits[n]},Divisible[Times@@idn,Total[idn]]]
Select[Range[500],okQ] (* Harvey P. Dale, Nov 24 2010 *)

PARI

is(n)=n&&prod(i=1,#n=digits(n),n[i])%vecsum(n)==0 \\ M. F. Hasler, Feb 28 2018

Extensions

Corrected by Vladeta Jovovic and Larry Reeves (larryr(AT)acm.org), Jun 08 2001

Erroneous 0 term removed by David A. Corneth, Jun 05 2016