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
Examples
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.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..160 (terms < 3*10^14)
- Giovanni Resta, Zuckerman numbers, Numbers Aplenty.
Crossrefs
Programs
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Mathematica
zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; Select[Range[10^6], zuckQ[#] && zuckQ[#/Times @@ IntegerDigits[#]] &] (* Amiram Eldar, Apr 26 2021 *)
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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
Extensions
More terms from David A. Corneth, Apr 26 2021
Comments