OFFSET
1,6
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
EXAMPLE
108 has in total 16 = A001055(108) factorizations:
Factors Are there any factors that are divisible by p^p,
where p is any prime?
-------------------------------------------------------------------
[3, 3, 3, 2, 2] No
[4, 3, 3, 3] Yes (4, divisible by 2^2)
[6, 3, 3, 2] No
[6, 6, 3] No
[9, 3, 2, 2] No
[9, 4, 3] Yes (4)
[9, 6, 2] No
[12, 3, 3] Yes (12, divisible by 2^2)
[12, 9] Yes (12)
[18, 3, 2] No
[18, 6] No
[27, 2, 2] Yes (27, divisible by 3^3)
[27, 4] Yes (both 27 and 4)
[36, 3] Yes (36)
[54, 2] Yes (54, divisible by 3^3)
[108] Yes (108 = 2^2 * 3^3)
Thus only seven of the factorizations satisfy the criterion, and a(108) = 7.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 16 2023
STATUS
approved