A343681 Zuckerman numbers which when divided by product of their digits, give a quotient which is also a Zuckerman number.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 36, 111, 128, 135, 144, 175, 384, 672, 735, 1111, 1296, 1575, 11111, 22176, 42624, 82944, 111111, 139968, 688128, 719712, 1111111, 1161216, 1492992, 2241792, 2794176, 4136832, 4741632, 6838272, 11111111, 12171264, 13395375, 13436928

Offset

1,2

Comments

Alternative Name: Zuckerman numbers k such that k/(product of digits of k) is also a Zuckerman number. - Wesley Ivan Hurt, Apr 26 2021

All positive repunits are terms (A002275).

Links

Giovanni Resta, Table of n, a(n) for n = 1..160 (terms < 3*10^14)

Giovanni Resta, Zuckerman numbers, Numbers Aplenty.

Example

24 is a Zuckerman number as 24/(2*4) = 3, 3/3 = 1 so 3 is also a Zuckerman number, and 24 is a term.
1296 is a Zuckerman number as 1296/(1*2*9*6) = 12, 12/(1*2) = 4 so 12 is also a Zuckerman number and 1296 is a term.

Mathematica

zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[10^6], zuckQ[#] && zuckQ[#/Times @@ IntegerDigits[#]] &] (* Amiram Eldar, Apr 26 2021 *)

Prog

(PARI) isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602
isok(n) = isz(n) && isz(n/vecprod(digits(n))); \\ Michel Marcus, Apr 26 2021

Crossrefs

Cf. A002275, A007602, A288069, A343680, A343682.

Cf. A235507 (similar, with Niven numbers).

Sequence in context: A064700 A180484 A007602 * A337941 A167620 A169935

Adjacent sequences: A343678 A343679 A343680 * A343682 A343683 A343684

Keyword

nonn,base

Author

Bernard Schott, Apr 26 2021

Extensions

More terms from David A. Corneth, Apr 26 2021

Status

approved