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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.
2
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
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.
Sequence in context: A087682 A104628 A045564 * A087142 A158019 A228205
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jun 24 2017
STATUS
approved