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

Author

Michel Lagneau, Aug 24 2018

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A001221, A080683, A097227, A290675.

Programs

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 *)