A174234 - OEIS

A174234

A variant of Landau's function (A000793) with a restriction on the length of cycles. a(n) is the largest value of lcm(p_1, ..., p_k), with p_1 + ... + p_k <= n, such that there exist integer offsets f_1, ..., f_k with 0 <= f_i < p_i, for which f_i and f_j are different modulo gcd(p_i, p_j).

%I #13 May 10 2019 11:06:44

%S 1,2,3,4,5,6,7,8,9,12,12,12,13,24,24,30,30,40,40,42,42,60,60,70,70,84,

%T 84,90,90,120,120,126,126,168,168,180,180,240,240,240,240,336,336,336,

%U 336,420,420,420,420,560,560,560,560,720,720,720

%N A variant of Landau's function (A000793) with a restriction on the length of cycles. a(n) is the largest value of lcm(p_1, ..., p_k), with p_1 + ... + p_k <= n, such that there exist integer offsets f_1, ..., f_k with 0 <= f_i < p_i, for which f_i and f_j are different modulo gcd(p_i, p_j).

%C a(n) is the maximal period of any set of nonintersecting congruences with moduli summing to at most n. - _Charlie Neder_, May 09 2019

%H Charlie Neder, <a href="/A174234/b174234.txt">Table of n, a(n) for n = 1..150</a>

%H A. Okhotin, <a href="http://tucs.fi/publications/insight.php?id=tOkhotin09a">"A study of unambiguous finite automata over a one-letter alphabet"</a>

%F Asymptotic: log a(n) ~ (n log(n)^2) ^ 1/3.

%e a(10)=12 is given by k=2, p_1=4, p_2=6, f_1=0 and f_2=1, with 0 != 1 mod(gcd(4, 6)).

%Y Cf. Landau's function (A000793).

%K more,nonn

%O 1,2

%A Alexander Okhotin (alexander.okhotin(AT)utu.fi), Mar 13 2010

%E a(51)-a(56) and minor edits from _Charlie Neder_, May 09 2019