A285271 Numbers that are divisible by each of their digits but that are not divisible by the sum of their digits or by the product of their digits.

11, 15, 22, 33, 44, 48, 55, 66, 77, 88, 99, 115, 122, 124, 126, 128, 155, 162, 168, 175, 184, 212, 222, 244, 248, 264, 288, 324, 333, 336, 366, 384, 396, 412, 424, 444, 448, 488, 515, 555, 636, 648, 666, 672, 728, 777, 784, 816, 824, 848, 864, 888, 936, 999, 1111, 1112

Offset

1,1

Comments

Numbers which are divisible by the sum and the product of their digits (A038186) are also divisible by each of their digits (A034838)

The product of the digits of n are trivially divisible by each digit; so if that product divides n, each digit must divide n. - Franklin T. Adams-Watters, Jul 02 2017

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1520

Example

15 is divisible by its digits 1 and 5, and 15 is divisible by the product of its digits 1*5 = 5, but 15 is not divisible by the sum of its digits 1+5 = 6, hence 15 is a term.
48 is divisible by its digits 4 and 8, and 48 is divisible by the sum of its digits 4+8 = 12, but 48 is not divisible by the product of its digits 4*8 = 32, hence 48 is a term.
124 is divisible by its digits 1, 2 and 4, but 124 is not divisible by the product of its digits 1*2*4 = 8 and 124 is not divisible by the sum of its digits 1+2+4 = 7, hence 124 is a term.
24 is divisible by its digits 2 and 4, and 24 is divisible by the sum of its digits 2+4 = 6, and 24 is also divisible by the product of its digits 2*4 = 8, hence 24 is NOT a term.

Maple

filter:= proc(n) local F;
   F:= convert(n, base, 10);
   andmap(t -> t > 0 and n mod t = 0, F) and not(n mod convert(F, `+`) = 0 and n mod convert(F, `*`) = 0)
end proc:
select(filter, [$11 .. 2000]); # Robert Israel, Jul 05 2017

Mathematica

fQ[n_] := Block[{ind = IntegerDigits@ n}, Union[ IntegerQ@# & /@ (n/ind)] == {True} && (!IntegerQ[n/Plus @@ ind] || !IntegerQ[n/Times @@ ind])]; Select[Range@ 1112, fQ] (* Robert G. Wilson v, Jul 05 2017 *)

Prog

(PARI) isok(n) = {d = digits(n); if (vecmin(d), for (k=1, #d, if (n % d[k], return (0)); ); return ((n % vecsum(d)) || (n % prod(k=1, #d, d[k]))); ); return (0); } \\ Michel Marcus, Jul 02 2017

Crossrefs

Subsequence of A034838.

Cf. A005349, A007602, A038186.

Sequence in context: A087682 A104628 A045564 * A087142 A158019 A228205

Adjacent sequences: A285268 A285269 A285270 * A285272 A285273 A285274

Keyword

nonn,base

Author

Bernard Schott, Jun 24 2017

Status

approved