A198375 -id:A198375 - cp's OEIS frontend

A198376 Largest n-digit number whose product of digits is n or 0 if no such number exists.

1, 21, 311, 4111, 51111, 611111, 7111111, 81111111, 911111111, 5211111111, 0, 621111111111, 0, 72111111111111, 531111111111111, 8211111111111111, 0, 921111111111111111, 0, 54111111111111111111, 731111111111111111111, 0, 0, 831111111111111111111111

Offset: 1

Jaroslav Krizek, Oct 23 2011

			113, 131, and 311 are the 3-digit numbers whose product of digits is 3; 311 is the largest.

Michael S. Branicky, Table of n, a(n) for n = 1..1000

Cf. A198375 (smallest), A002473, A068191.

Table[If[FactorInteger[n][[-1, 1]] > 9, 0, i = (10^n - 1)/9; While[i < 10^n && Times @@ (d = IntegerDigits[i]) != n, i++]; If[i == 10^n, 0, FromDigits[Reverse[d]]]], {n, 30}] (* T. D. Noe, Oct 24 2011 *)

def A198376(n):
  ncopy, p, an = n, 1, ""
  for d in range(9, 1, -1):
    while ncopy%d == 0: ncopy//=d; p *= d; an += str(d)
  if p == n and len(an) <= n: return int(an+'1'*(n-len(an)))
  return 0
print([A198376(n) for n in range(1, 25)]) # Michael S. Branicky, Jan 21 2021

a(A068191(n)) = 0 for n >=1.

a(n) <> 0 iff n in { A002473 }. - Michael S. Branicky, Jan 21 2021

A221644 Let abcd... be the decimal expansion of k. Sequence lists numbers k such that 1/a + 2/b + 3/c + 4/d + ... is an integer.

Original entry on oeis.org

1, 11, 12, 24, 33, 111, 113, 121, 123, 139, 142, 146, 155, 184, 212, 216, 222, 226, 241, 243, 331, 333, 369, 414, 424, 482, 486, 649, 662, 666, 848, 1111, 1112, 1114, 1128, 1131, 1132, 1134, 1168, 1177, 1196, 1211, 1212, 1214, 1228, 1231, 1232, 1234, 1268

Offset: 1

Michel Lagneau, Aug 08 2013

The repunits numbers 1, 11, 111, 1111, ... (A002275) are in the sequence.
The first nine terms 1, 12, 123, 1234, ... of A007908 are in the sequence.
If a number of the form ab1 is in the sequence, the corresponding number of the form ab3 is also in the sequence.
If a number of the form abc1 is in the sequence, the corresponding number of the form abc2 is also in the sequence.
If a number of the form abc11 is in the sequence, the corresponding number of the form abc15 is also in the sequence.
The first nine terms 1, 12, 113, 1114, 11115, ... of A198375 are in the sequence.
In the general case, if n = abcd...q is in the sequence where q is the k-th decimal digit of n, the number abcd...qr is also in the sequence if k+1 is divisible by r; for example, 82812 is in the sequence => 828121, 828122, 828123 and 828126 are also in the sequence because 6 is divisible by 1, 2, 3 and 6.

			184 is in the sequence because 1/1 + 2/8 + 3/4 = 2.

Michel Lagneau, Table of n, a(n) for n = 1..10000

Cf. A002275, A007908, A198375.

with(numtheory):for n from 1 to 2000 do: d:=convert(n, base, 10):n1:=nops(d):p:=product('d[i]', 'i'=1..n1):if p<>0 then s:=sum('i/d[n1-i+1] ', 'i'=1..n1):if s=floor(s) then printf(`%d, `,n):else fi:fi:od:

Select[Range[1300],FreeQ[IntegerDigits[#],0]&&IntegerQ[Total[ Range[ IntegerLength[ #]]/ IntegerDigits[ #]]]&] (* Harvey P. Dale, May 16 2018 *)

isok(n) = my(d=digits(n)); vecmin(d) && (denominator(sum(k=1, #d, k/d[k])) == 1); \\ Michel Marcus, Sep 14 2017

cp's OEIS Frontend

A198376 Largest n-digit number whose product of digits is n or 0 if no such number exists.

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