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).

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, 84, 90, 90, 120, 120, 126, 126, 168, 168, 180, 180, 240, 240, 240, 240, 336, 336, 336, 336, 420, 420, 420, 420, 560, 560, 560, 560, 720, 720, 720, 720, 880, 880, 880

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Examples

			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)).
		

Links

• Charlie Neder, Table of n, a(n) for n = 1..150
• A. Okhotin, "A study of unambiguous finite automata over a one-letter alphabet"

Crossrefs

Cf. Landau's function (A000793).

Formula

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

Extensions

a(51) onwards and minor edits from Charlie Neder, May 09 2019