A384502 - OEIS

%I #47 Aug 16 2025 10:04:47

%S 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,

%T 21,21,21,21,23,23,23,23,25,25,25,25,27,27,27,27,29,29,29,29,31,31,31,

%U 31,33,33,33,33,34,35,35,35,35,37,37,37,37,39,39,39,39,39,41

%N 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.

%H David A. Corneth, <a href="/A384502/b384502.txt">Table of n, a(n) for n = 4..704</a>

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

%e 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.

%Y Cf. A067175, A001221, A221054, A383858.

%K nonn,base

%O 4,1

%A _Jean-Marc Rebert_, May 31 2025

%E a(11)-a(59) from _Sean A. Irvine_, Jun 23 2025

%E More terms from _David A. Corneth_, Aug 15 2025