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

1,1

Comments

All numbers in this sequence are composite.

Links

Table of n, a(n) for n=1..46.

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

Cf. A002808, A025283, A074211.

Sequence in context: A350735 A073954 A227868 * A176876 A257767 A158136

Adjacent sequences: A353056 A353057 A353058 * A353060 A353061 A353062

Keyword

nonn,base

Author

Tanya Khovanova, Apr 20 2022

Status

approved