%I #16 May 07 2022 10:27:24
%S 143,187,341,351,451,671,781,1023,1024,1057,1207,1243,1324,1352,1372,
%T 1375,1379,1703,1982,2139,2176,2189,2317,2321,2510,2519,2816,3051,
%U 3125,3159,3375,3421,3641,3861,4232,5102,5210,6182,6272,7819,8197,8921,9251,9317,9481,9531
%N Integers k such that the prime factorization of k uses digits from a proper subset of the digits of k.
%C All numbers in this sequence are composite.
%e 143 = 11^1 * 13^1: the number itself uses digits 1, 3, and 4, while the prime factorization uses the subset of digits: 1 and 3. Thus, 143 is in this sequence.
%e 25 = 5^2. Both the number and the prime factorization use the same set of digits. Thus, 25 is not in this sequence.
%t Select[Range[10000], SubsetQ[Union[IntegerDigits[#]], Union[Flatten[IntegerDigits[FactorInteger[#]]]]] && Length[Union[IntegerDigits[#]]] > Length[Union[Flatten[IntegerDigits[FactorInteger[#]]]]] &]
%o (Python)
%o from sympy import factorint
%o def ok(n): return set("".join(str(p)+str(e) for p, e in factorint(n).items())) < set(str(n))
%o print([k for k in range(2, 9999) if ok(k)]) # _Michael S. Branicky_, Apr 20 2022
%Y Cf. A002808, A025283, A074211.
%K nonn,base
%O 1,1
%A _Tanya Khovanova_, Apr 20 2022