A318298 - OEIS

%I #19 Sep 05 2018 09:57:57

%S 12,14,154,1196,14112,21888,53625,226512,279174,358435,821142,1222452,

%T 1665664,2228814,2454375,2614248,2872116,4425729,5751746,8653645,

%U 9551256,15261246,19427226,19644898,19775998,21271488,27676935,29591892,29956212,41878242,45574144

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

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

%C 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.

%H Giovanni Resta, <a href="/A318298/b318298.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p with(numtheory):nn:=10^8:

%p for n from 1 to nn do:

%p lst:={}:d:=factorset(n):n0:=nops(d):

%p q:=convert(n,base,10):n1:=nops(q):

%p p:=product(‘q[i]’, ‘i’=1..n1):

%p if p<>0

%p   then

%p   for i from 1 to n1 do :

%p    lst:=lst union {ithprime(q[i])}:

%p   od:

%p    if lst = d

%p     then

%p      print(n):

%p      else

%p      fi:fi:

%p od:

%t 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 *)

%Y Cf. A001221, A080683, A097227, A290675.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Aug 24 2018