A384502 Maximum number of distinct prime factors in an n-digit number, n > 3, where its set of distinct prime factors can be partitioned into two equal-sum subsets, each containing at least two elements.
5, 5, 7, 7, 7, 9, 9, 9, 11, 11, 11, 13, 13, 13, 15, 15, 15, 16, 17, 17, 17, 19, 19, 19, 19, 21, 21, 21, 21, 23, 23, 23, 23, 25, 25, 25, 25, 27, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 31, 33, 33, 33, 33, 34, 35, 35, 35, 35, 37, 37, 37, 37, 39, 39, 39, 39, 39, 41
Offset: 4
Examples
a(4) = 5, since 2310 = 2 * 3 * 5 * 7 * 11 is a 4-digit number with omega(2310) = 5, and its prime factors can be split into two equal-sum parts: 2 + 5 + 7 = 3 + 11. No 4-digit number that meets this partitioning criterion has an omega value exceeding 5.
Links
- David A. Corneth, Table of n, a(n) for n = 4..704
Formula
a(n) <= (largest m such that A067175(m) <= n).
Extensions
a(11)-a(59) from Sean A. Irvine, Jun 23 2025
More terms from David A. Corneth, Aug 15 2025