

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



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
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OFFSET

1,2


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


LINKS

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


FORMULA

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


EXAMPLE

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)).


CROSSREFS

Cf. Landau's function (A000793).
Sequence in context: A029970 A143265 A109841 * A163807 A118766 A136399
Adjacent sequences: A174231 A174232 A174233 * A174235 A174236 A174237


KEYWORD

more,nonn


AUTHOR

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


EXTENSIONS

a(51)a(56) and minor edits from Charlie Neder, May 09 2019


STATUS

approved



