cp's OEIS Frontend

A342650 Numbers divisible both by their nonzero individual digits and by the sum of their digits.

%I A342650 #22 Mar 18 2021 05:57:35
%S A342650 1,2,3,4,5,6,7,8,9,10,12,20,24,30,36,40,48,50,60,70,80,90,100,102,110,
%T A342650 111,112,120,126,132,135,140,144,150,162,200,204,210,216,220,222,224,
%U A342650 240,264,280,288,300,306,312,315,324,330,333,336,360,396,400,408,420,432,440,444,448,480,500
%N A342650 Numbers divisible both by their nonzero individual digits and by the sum of their digits.
%C A342650 Equivalently, Niven numbers that are divisible by their nonzero digits. A Niven number (A005349) is a number that is divisible by the sum of its digits.
%C A342650 Niven numbers without zero digit that are divisible by their individual digits are in A051004.
%C A342650 Differs from super Niven numbers, the first 25 terms are the same, then A328273(26) = 120 while a(26) = 111.
%C A342650 This sequence is infinite since if m is a term, then 10*m is another term.
%e A342650 102 is divisible by its nonzero digits 1 and 2, and 102 is also divisible by the sum of its digits 1 + 0 + 2 = 3, then 102 is a term.
%t A342650 q[n_] := AllTrue[(d = IntegerDigits[n]), # == 0 || Divisible[n, #] &] && Divisible[n, Plus @@ d]; Select[Range[500], q] (* _Amiram Eldar_, Mar 18 2021 *)
%o A342650 (PARI) isok(m) = if (!(m % sumdigits(m)), my(d=select(x->(x>0), Set(digits(m)))); setintersect(d, divisors(m)) == d); \\ _Michel Marcus_, Mar 18 2021
%Y A342650 Intersection of A002796 and A005349.
%Y A342650 Supersequence of A051004.
%Y A342650 Cf. A034838, A328273.
%K A342650 nonn,base
%O A342650 1,2
%A A342650 _Bernard Schott_, Mar 18 2021