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A342262 Numbers divisible both by the product of their nonzero digits (A055471) and by the sum of their digits (A005349). 1
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 20, 24, 30, 36, 40, 50, 60, 70, 80, 90, 100, 102, 110, 111, 112, 120, 132, 135, 140, 144, 150, 200, 210, 216, 220, 224, 240, 300, 306, 312, 315, 360, 400, 432, 480, 500, 510, 540, 550, 600, 612, 624, 630, 700, 735, 800, 900, 1000, 1002, 1008 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

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

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

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..61.

EXAMPLE

306 = (3*6) * 17 is divisible by the product of its nonzero digits and 306 = (3+0+6) * 34 is also divisible by the sum its digits, hence 306 is a term.

MATHEMATICA

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

PROG

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

CROSSREFS

Intersection of A005349 and A055471.

Supersequence of A038186.

Cf. A051004, A328273, A342650.

Sequence in context: A271955 A342650 A328273 * A255734 A033075 A215014

Adjacent sequences:  A342259 A342260 A342261 * A342263 A342264 A342265

KEYWORD

nonn,base

AUTHOR

Bernard Schott, Mar 27 2021

STATUS

approved

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Last modified September 18 22:29 EDT 2021. Contains 347548 sequences. (Running on oeis4.)