A353059 Integers k such that the prime factorization of k uses digits from a proper subset of the digits of k.
143, 187, 341, 351, 451, 671, 781, 1023, 1024, 1057, 1207, 1243, 1324, 1352, 1372, 1375, 1379, 1703, 1982, 2139, 2176, 2189, 2317, 2321, 2510, 2519, 2816, 3051, 3125, 3159, 3375, 3421, 3641, 3861, 4232, 5102, 5210, 6182, 6272, 7819, 8197, 8921, 9251, 9317, 9481, 9531
Offset: 1
Examples
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. 25 = 5^2. Both the number and the prime factorization use the same set of digits. Thus, 25 is not in this sequence.
Programs
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Mathematica
Select[Range[10000], SubsetQ[Union[IntegerDigits[#]], Union[Flatten[IntegerDigits[FactorInteger[#]]]]] && Length[Union[IntegerDigits[#]]] > Length[Union[Flatten[IntegerDigits[FactorInteger[#]]]]] &]
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Python
from sympy import factorint def ok(n): return set("".join(str(p)+str(e) for p, e in factorint(n).items())) < set(str(n)) print([k for k in range(2, 9999) if ok(k)]) # Michael S. Branicky, Apr 20 2022
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