A380442 - OEIS

A380442

a(n) is the largest Frobenius number of three distinct relatively prime numbers that sum to n.

1, 1, 3, 2, 5, 7, 7, 11, 13, 11, 17, 19, 23, 23, 29, 31, 35, 39, 43, 47, 51, 47, 59, 63, 67, 71, 79, 83, 89, 95, 101, 107, 113, 103, 125, 131, 139, 143, 153, 155, 167, 175, 181, 191, 199, 199, 215, 223, 233, 239, 251, 259, 269, 279, 289, 299, 309, 311, 329, 339

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OFFSET

9,3

COMMENTS

6 is the smallest number that can be partitioned into three distinct positive integers excluding n = 1 through 5.

a(6) would be -1 as the only partition of 6 into 3 distinct numbers that are relatively prime are (1, 2, 3) and the largest Frobenius number of that partition is -1.

Similarly a(7) and a(8) would be -1 as all partitions of these numbers into three distinct parts have a 1 in them.

LINKS

Table of n, a(n) for n=9..68.

Brady Haran and David Eisenbud, The Frobenius Problem (and numerical semigroups) - Numberphile, Numberphile video, 2025

EXAMPLE

a(11) = 3 as the partitions of 11 into 3 distinct numbers that are relatively prime are (2,4,5) and (2,3,6) that have Frobenius number 3 and 1 respectively and their maximum is 3.

CROSSREFS

Cf. A386243.

Sequence in context: A325985 A151749 A175911 * A394458 A337405 A304881

Adjacent sequences: A380439 A380440 A380441 * A380443 A380444 A380445

KEYWORD

nonn

AUTHOR

David A. Corneth, Jul 25 2025

STATUS

approved