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

Author

Tanya Khovanova, Apr 20 2022

Keywords

• nonn
• base

Comments

All numbers in this sequence are composite.

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.
		

Crossrefs

Cf. A002808, A025283, A074211.

Programs

Mathematica

Select[Range[10000], SubsetQ[Union[IntegerDigits[#]], Union[Flatten[IntegerDigits[FactorInteger[#]]]]] && Length[Union[IntegerDigits[#]]] > Length[Union[Flatten[IntegerDigits[FactorInteger[#]]]]] &]

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