cp's OEIS Frontend

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

%I A318298 #19 Sep 05 2018 09:57:57
%S A318298 12,14,154,1196,14112,21888,53625,226512,279174,358435,821142,1222452,
%T A318298 1665664,2228814,2454375,2614248,2872116,4425729,5751746,8653645,
%U A318298 9551256,15261246,19427226,19644898,19775998,21271488,27676935,29591892,29956212,41878242,45574144
%N A318298 Numbers whose set of decimal digits coincides with the set of the indices of their prime factors.
%C A318298 It is impossible to find a number with 9 distinct decimal digits because the prime factors 2 and 5 generate d_k = 0.
%C A318298 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 A318298 Giovanni Resta, <a href="/A318298/b318298.txt">Table of n, a(n) for n = 1..10000</a>
%e A318298 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 A318298 with(numtheory):nn:=10^8:
%p A318298 for n from 1 to nn do:
%p A318298 lst:={}:d:=factorset(n):n0:=nops(d):
%p A318298 q:=convert(n,base,10):n1:=nops(q):
%p A318298 p:=product(‘q[i]’, ‘i’=1..n1):
%p A318298 if p<>0
%p A318298   then
%p A318298   for i from 1 to n1 do :
%p A318298    lst:=lst union {ithprime(q[i])}:
%p A318298   od:
%p A318298    if lst = d
%p A318298     then
%p A318298      print(n):
%p A318298      else
%p A318298      fi:fi:
%p A318298 od:
%t A318298 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 A318298 Cf. A001221, A080683, A097227, A290675.
%K A318298 nonn,base
%O A318298 1,1
%A A318298 _Michel Lagneau_, Aug 24 2018