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