maximal factor partitions

[hv at crypt.org]

As mentioned earlier, I needed to calculate maximal factor partitions to
determine whether there was any hope of A1055(n) >= n-1 for some n.
It would appear not: max(A1055(n)) grows much more slowly than n, with my
calcalation reaching A1055(9676800) = 124207.

Not sure how interesting they are, but the results are sequences:

%I A000001
%S A000001 1 4 8 12 16 24 36 48 72 96 120 144 192 216 240 288 360 432 480 576
%T A000001 720 960 1080 1152 1440 2160 2880 4320 5040 5760 7200 8640 10080
%U A000001 11520 12960 14400 15120 17280 20160 25920 28800 30240 34560 40320
%N A000001 maximal factor partitions: A001055(a(n)) is greater than any previous value
%e A000001 12 can be partitioned four ways: (12, 2 * 6, 3 * 4, 2 * 2 * 3); no smaller number can be partitioned that many ways, so 12 is included in the sequence
%C A000001 a(n) is necessarily a subsequence of A025487
%Y A000001 Cf. A000002 for the corresponding number of partitions
%K A000001 nonn,easy
%O A000001 0,2
%A A000001 hv at crypt.org (Hugo van der Sanden)

%I A000002
%S A000002 1 2 3 4 5 7 9 12 16 19 21 29 30 31 38 47 52 57 64 77 98 105 109 118
%T A000002 171 212 289 382 392 467 484 662 719 737 783 843 907 1097 1261 1386
%U A000002 1397 1713 1768 2116 2179 2343 3079 3444 3681 3930 5288 5413 5447
%N A000002 maximal factor partitions: when these numbers first appear in A001055 each is the highest value seen so far
%e A000002 12 can be partitioned four ways: (12, 2 * 6, 3 * 4, 2 * 2 * 3); no smaller number can be partitioned that many ways, so 4 is included in the sequence
%Y A000002 Cf. A000001 for the corresponding number being partitioned
%K A000002 nonn,easy
%O A000002 0,2
%A A000002 hv at crypt.org (Hugo van der Sanden)

Hugo