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A353059
Integers k such that the prime factorization of k uses digits from a proper subset of the digits of k.
0
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
1,1
COMMENTS
All numbers in this sequence are composite.
EXAMPLE
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.
MATHEMATICA
Select[Range[10000], SubsetQ[Union[IntegerDigits[#]], Union[Flatten[IntegerDigits[FactorInteger[#]]]]] && Length[Union[IntegerDigits[#]]] > Length[Union[Flatten[IntegerDigits[FactorInteger[#]]]]] &]
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Tanya Khovanova, Apr 20 2022
STATUS
approved