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

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, 111, 112, 120, 126, 132, 135, 140, 144, 150, 162, 200, 204, 210, 216, 220, 222, 224, 240, 264, 280, 288, 300, 306, 312, 315, 324, 330, 333, 336, 360, 396, 400, 408, 420, 432, 440, 444, 448, 480, 500

Offset

1,2

Comments

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.

Niven numbers without zero digit that are divisible by their individual digits are in A051004.

Differs from super Niven numbers, the first 25 terms are the same, then A328273(26) = 120 while a(26) = 111.

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

Links

Table of n, a(n) for n=1..65.

Example

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.

Mathematica

q[n_] := AllTrue[(d = IntegerDigits[n]), # == 0 || Divisible[n, #] &] && Divisible[n, Plus @@ d]; Select[Range[500], q] (* Amiram Eldar, Mar 18 2021 *)

Prog

(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

Crossrefs

Intersection of A002796 and A005349.

Supersequence of A051004.

Cf. A034838, A328273.

Sequence in context: A180468 A271955 A365420 * A328273 A342262 A255734

Adjacent sequences: A342647 A342648 A342649 * A342651 A342652 A342653

Keyword

nonn,base

Author

Bernard Schott, Mar 18 2021

Status

approved