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A318298 Numbers whose set of decimal digits coincides with the set of the indices of their prime factors. 2
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 (list; graph; refs; listen; history; text; internal format)
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(ā€˜q[i]ā€™, ā€˜iā€™=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

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Last modified August 11 04:00 EDT 2020. Contains 336421 sequences. (Running on oeis4.)