cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A288069 Quotients obtained when the Zuckerman numbers are divided by the product of their digits.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 6, 3, 3, 2, 111, 56, 23, 8, 22, 9, 9, 5, 53, 18, 14, 52, 21, 4, 18, 51, 13, 8, 7, 17, 1111, 556, 371, 223, 186, 377, 28, 37, 19, 303, 12, 437, 74, 28, 59, 9, 49, 528, 67, 93, 27, 1037, 174, 22, 151, 13, 184, 29, 514, 66, 46
Offset: 1

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Author

Bernard Schott, Jun 05 2017

Keywords

Comments

The Zuckerman numbers (A007602) are the numbers that are divisible by the product of their digits.
Question: Is A067251 a subsequence? No, it appears in A056770 that not all integers other than multiples of 10 can be obtained as quotient, such as 15, 16, 24, 25, 26, 32, .... (see A342941).
The limit of the sequence is infinite: for any x, there is some N such that, for all n > N, a(n) > x. Proof: a Zuckerman number with d digits is at least 10^(d-1) and has a digit product at most 9^d and so has a quotient at least 10^(d-1)/9^d which goes to infinity with d. - Charles R Greathouse IV, Jun 05 2017
The repunits A002275 are a subsequence. - Peter Schorn, Apr 05 2025

Examples

			a(11) = 12/(1*2) = 6; a(13) = 24/(2*4) = 3.
		

Crossrefs

Programs

  • Maple
    f:= proc(n) local L,p;
       p:= convert(convert(n,base,10),`*`);
       if p > 0 then
         if n mod p = 0 then return n/p fi
       fi
    end proc:
    map(f, [$1..10^4]); # Robert Israel, Jun 05 2017
  • Mathematica
    Select[Table[n/Max[Times@@IntegerDigits[n],Pi/100],{n,5000}],IntegerQ] (* Harvey P. Dale, Aug 16 2021 *)
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