A343680 -id:A343680 - cp's OEIS frontend

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

Bernard Schott, Apr 26 2021

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).

			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.

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

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

Cf. A235507 (similar, with Niven numbers).

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

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

More terms from David A. Corneth, Apr 26 2021

A343682 Zuckerman numbers which when divided by the product of their digits, give a quotient which is a Niven (Harshad) number.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 24, 36, 111, 128, 135, 144, 175, 216, 315, 384, 432, 672, 735, 1296, 1575, 2916, 11115, 11232, 11664, 12132, 12288, 12312, 13212, 13824, 14112, 16416, 22176, 23112, 23328, 26112, 27216, 31212, 32832, 34272, 34992, 42624, 72128, 77175

Offset: 1

Bernard Schott, Apr 26 2021

Repunit R(k) is a term iff k divides R(k) (A014950).

			36 is a Zuckerman number as 36/(3*6) = 2, 2/2 = 1 that is a Niven number, and 36 is a term.
315 is a Zuckerman number as 315/(3*1*5) = 21, 21/(2+1) = 7 that is a Niven number, and 315 is a term.

Giovanni Resta, Zuckerman numbers, Numbers Aplenty.

Cf. A005349, A007602, A235507, A288069, A343680, A343681.

nivenQ[n_] := IntegerQ[n] && (sum = Plus @@ IntegerDigits[n]) > 0 && Divisible[n, sum]; Select[Range[10^5], (prod = Times @@ IntegerDigits[#]) > 0 && nivenQ[# / prod] &] (* Amiram Eldar, Apr 26 2021 *)

isn(n) = !(n%sumdigits(n)); \\ A005349
isz(n) = my(p=vecprod(digits(n))); p && !(n % p); \\ A007602
isok(n) = isz(n) && isn(n/vecprod(digits(n))); \\ Michel Marcus, Apr 26 2021

More terms from Michel Marcus, Apr 26 2021

cp's OEIS Frontend

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

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