cp's OEIS Frontend

A342262 Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).

%I A342262 #25 Sep 26 2021 18:49:48
%S A342262 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 A342262 111,112,120,132,135,140,144,150,200,210,216,220,224,240,300,306,312,
%U A342262 315,360,400,432,480,500,510,540,550,600,612,624,630,700,735,800,900,1000,1002,1008
%N A342262 Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349).
%C A342262 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 A342262 Niven numbers without zero digit that are divisible by the product of their digits are in A038186.
%C A342262 Differs from super Niven numbers, the first 16 terms are the same, then A328273(17) = 48 while a(17) = 50.
%C A342262 This sequence is infinite since if m is a term, then 10*m is another term.
%H A342262 Harvey P. Dale, <a href="/A342262/b342262.txt">Table of n, a(n) for n = 1..1000</a>
%e A342262 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 A342262 q[n_] := And @@ Divisible[n, {Times @@ (d = Select[IntegerDigits[n], # > 0 &]), Plus @@ d}]; Select[Range[1000], q] (* _Amiram Eldar_, Mar 27 2021 *)
%t A342262 Select[Range[1200],Mod[#,Times@@(IntegerDigits[#]/.(0->1))]== Mod[#,Total[ IntegerDigits[#]]]==0&] (* _Harvey P. Dale_, Sep 26 2021 *)
%o A342262 (PARI) isok(m) = my(d=select(x->(x!=0), digits(m))); !(m % vecprod(d)) && !(m % vecsum(d)); \\ _Michel Marcus_, Mar 27 2021
%Y A342262 Intersection of A005349 and A055471.
%Y A342262 Supersequence of A038186.
%Y A342262 Cf. A051004, A328273, A342650.
%K A342262 nonn,base
%O A342262 1,2
%A A342262 _Bernard Schott_, Mar 27 2021
%E A342262 Example clarified by _Harvey P. Dale_, Sep 26 2021