A055931 -id:A055931 - cp's OEIS frontend

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

Felice Russo

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

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

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

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

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

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

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

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

A061013 Numbers k such that (product of digits of k) is divisible by (sum of digits of k), where 0's are not permitted.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 36, 44, 63, 66, 88, 123, 132, 138, 145, 154, 159, 167, 176, 183, 189, 195, 198, 213, 224, 231, 235, 242, 246, 253, 257, 264, 268, 275, 279, 286, 297, 312, 318, 321, 325, 333, 345, 347, 352, 354, 357, 369, 374, 375, 381, 396, 415

Offset: 1

Heiner Muller-Merbach (hmm(AT)sozwi.uni-kl.de), Jun 06 2001

Called "perfect years". 1998 and 2114 are the nearest past and future examples.

			1998 is perfect since 1*9*9*8/(1+9+9+8) = 24.

H. Herles, Reformstau, Gefuehlsstau, Verkehrsstau. Generalanzeiger, 12/31/1997, p. V.
H. Muller-Merbach and L. Logelix, Perfekte Jahre, Technologie und Management, Vol. 42, 1993, No. 1, p. 47 and No. 2, p. 95.

David A. Corneth, Table of n, a(n) for n = 1..10000
H. Muller-Merbach, Wunsche für das "perfekte Jahr" 1998

See A038367 for case where 0 digits are allowed. Cf. A055931.

Cf. A274124.

for n from 1 to 3000 do a := convert(n,base,10):s := add(a[i],i=1..nops(a)):p := mul(a[i],i=1..nops(a)): if p<>0 and p mod s=0 then printf(`%d,`,n):fi:od:

Select[Range[415], FreeQ[x = IntegerDigits[#], 0] && Divisible[Times @@ x, Plus @@ x] &] (* Jayanta Basu, Jul 13 2013 *)

is(n) = my(d = digits(n)); vd = vecprod(d); vd != 0 && vd % vecsum(d) == 0 \\ David A. Corneth, Mar 15 2021

from math import prod
def ok(n):
    d = list(map(int, str(n)))
    pod, sod = prod(d), sum(d)
    return pod and pod%sod == 0
print([k for k in range(416) if ok(k)]) # Michael S. Branicky, Mar 28 2022

More terms from Larry Reeves (larryr(AT)acm.org) and Vladeta Jovovic, Jun 07 2001

cp's OEIS Frontend

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

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