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Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).
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%I #25 Sep 26 2021 18:49:48

%S 1,2,3,4,5,6,7,8,9,10,12,20,24,30,36,40,50,60,70,80,90,100,102,110,

%T 111,112,120,132,135,140,144,150,200,210,216,220,224,240,300,306,312,

%U 315,360,400,432,480,500,510,540,550,600,612,624,630,700,735,800,900,1000,1002,1008

%N Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).

%C Equivalently, Niven numbers that are divisible by the product of their nonzero digits. A Niven number (A005349) is a number that is divisible by the sum of its digits.

%C Niven numbers without zero digit that are divisible by the product of their digits are in A038186.

%C Differs from super Niven numbers, the first 16 terms are the same, then A328273(17) = 48 while a(17) = 50.

%C This sequence is infinite since if m is a term, then 10*m is another term.

%H Harvey P. Dale, <a href="/A342262/b342262.txt">Table of n, a(n) for n = 1..1000</a>

%e The product of the nonzero digits of 306 = 3*6 = 18, and 306 divided by 18 = 17. The sum of the digits of 306 = 3 + 0 + 6 = 9, and 306 divided by 9 = 34. Thus 306 is a term.

%t q[n_] := And @@ Divisible[n, {Times @@ (d = Select[IntegerDigits[n], # > 0 &]), Plus @@ d}]; Select[Range[1000], q] (* _Amiram Eldar_, Mar 27 2021 *)

%t Select[Range[1200],Mod[#,Times@@(IntegerDigits[#]/.(0->1))]== Mod[#,Total[ IntegerDigits[#]]]==0&] (* _Harvey P. Dale_, Sep 26 2021 *)

%o (PARI) isok(m) = my(d=select(x->(x!=0), digits(m))); !(m % vecprod(d)) && !(m % vecsum(d)); \\ _Michel Marcus_, Mar 27 2021

%Y Intersection of A005349 and A055471.

%Y Supersequence of A038186.

%Y Cf. A051004, A328273, A342650.

%K nonn,base

%O 1,2

%A _Bernard Schott_, Mar 27 2021

%E Example clarified by _Harvey P. Dale_, Sep 26 2021