A318298 Numbers whose set of decimal digits coincides with the set of the indices of their prime factors.

12, 14, 154, 1196, 14112, 21888, 53625, 226512, 279174, 358435, 821142, 1222452, 1665664, 2228814, 2454375, 2614248, 2872116, 4425729, 5751746, 8653645, 9551256, 15261246, 19427226, 19644898, 19775998, 21271488, 27676935, 29591892, 29956212, 41878242, 45574144

Offset

1,1

Comments

It is impossible to find a number with 9 distinct decimal digits because the prime factors 2 and 5 generate d_k = 0.

The finite subsequence containing the smallest numbers having at least j distinct digits for j = 2, 3, ..., 8, is 12, 154, 53625, 279174, 19427226, 82447365 and 41762985264.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

1196 is in the sequence because the prime factors are {2, 13, 23} = {prime(1), prime(6), prime(9)}, and 1196 contains the decimal digits 1, 6, 9.

Maple

with(numtheory):nn:=10^8:
for n from 1 to nn do:
lst:={}:d:=factorset(n):n0:=nops(d):
q:=convert(n, base, 10):n1:=nops(q):
p:=product(‘q[i]’, ‘i’=1..n1):
if p<>0
  then
  for i from 1 to n1 do :
   lst:=lst union {ithprime(q[i])}:
  od:
   if lst = d
    then
     print(n):
     else
     fi:fi:
od:

Mathematica

ok[n_] := Block[{f = First /@ FactorInteger[n], d}, Last@f < 24 && Min[d = Union@ IntegerDigits@ n] > 0 && Prime[d] == f]; Select[Range[10^6], ok] (* Giovanni Resta, Aug 24 2018 *)

Crossrefs

Cf. A001221, A080683, A097227, A290675.

Sequence in context: A058951 A287916 A002926 * A139310 A221819 A329026

Adjacent sequences: A318295 A318296 A318297 * A318299 A318300 A318301

Keyword

nonn,base

Author

Michel Lagneau, Aug 24 2018

Status

approved