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A290675 For a given n, the nonzero digits of n are the prime indices for the factorization of n.

%I A290675 #33 May 11 2023 12:11:45
%S A290675 14,154,1196,66079,279174,302768895,2249805789
%N A290675 For a given n, the nonzero digits of n are the prime indices for the factorization of n.
%C A290675 a(8) > 10^35, if it exists. - _Giovanni Resta_, Aug 09 2017
%C A290675 a(n) != 1 mod 10. a(8) > 10^44, if it exists. - _Chai Wah Wu_, Aug 10 2017
%C A290675 Fixed points of A113581. - _Alois P. Heinz_, May 11 2023
%e A290675 14 = 2*7, which are the 1st and 4th primes. 154 = 2*11*7 which are the 1st, 5th, and 4th primes, respectively. So use the digits of n (excluding zero) to find the corresponding primes, and the product of those primes equals n.
%t A290675 x = 10^7; (* this number is the upper end of the search *) Do[If[n == Times @@ Prime /@ DeleteCases[RealDigits[n][[1]], 0], Print[n]], {n, x}] (* or *)
%t A290675 up = 3*^9; ric[n_, e_, k_] := Block[{m=n, j=0}, If[k == 10, If[Most@ DigitCount[n] == e, Print@n; Sow@n], While[m < up, ric[m, Append[e, j], k+1]; j++; m *= Prime[k] ]]]; Sort@ Reap[ric[1, {}, 1]][[2, 1]] (* faster, _Giovanni Resta_, Aug 09 2017 *)
%o A290675 (PARI) is(n) = my(d=digits(n), prd=1); for(k=1, #d, if(d[k]!=0, prd=prd*prime(d[k]))); prd==n \\ _Felix Fröhlich_, Aug 09 2017
%o A290675 (Python)
%o A290675 from functools import reduce
%o A290675 from operator import mul
%o A290675 from itertools import combinations_with_replacement
%o A290675 A290675_list, lmax, ptuple = [], 12, (2,3,5,7,11,13,17,19,23)
%o A290675 for l in range(1,lmax+1):
%o A290675     for d in combinations_with_replacement(range(1,10),l):
%o A290675         n = reduce(mul,(ptuple[i-1] for i in d))
%o A290675         if n < 10**lmax and tuple(sorted((int(x) for x in str(n) if x != '0'))) == d:
%o A290675             A290675_list.append(n) # _Chai Wah Wu_, Aug 10 2017
%Y A290675 Supersequence of A097227.
%Y A290675 Cf. A113581.
%K A290675 nonn,hard,base
%O A290675 1,1
%A A290675 _Charles Ronco_, Aug 08 2017
%E A290675 a(6)-a(7) from _Giovanni Resta_, Aug 09 2017