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

4,1

Links

David A. Corneth, Table of n, a(n) for n = 4..704

Formula

a(n) <= (largest m such that A067175(m) <= n).

Example

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.

Crossrefs

Cf. A067175, A001221, A221054, A383858.

Sequence in context: A133888 A244587 A111186 * A127798 A053671 A028278

Adjacent sequences: A384499 A384500 A384501 * A384503 A384504 A384505

Keyword

nonn,base

Author

Jean-Marc Rebert, May 31 2025

Extensions

a(11)-a(59) from Sean A. Irvine, Jun 23 2025

More terms from David A. Corneth, Aug 15 2025

Status

approved