A350640 a(n) is the minimum lcm of the part sizes of a partition of n into parts of size 3 or more.

3, 4, 5, 3, 7, 4, 3, 5, 11, 3, 12, 7, 3, 4, 12, 3, 12, 4, 3, 11, 12, 3, 5, 12, 3, 4, 12, 3, 12, 4, 3, 12, 5, 3, 12, 12, 3, 4, 12, 3, 12, 4, 3, 12, 12, 3, 7, 5, 3, 4, 12, 3, 5, 4, 3, 12, 12, 3, 12, 12, 3, 4, 5, 3, 12, 4, 3, 5, 12, 3, 12, 12, 3, 4, 7, 3, 12, 4

Offset

3,1

Comments

Equivalently, a(n) is the minimum order of a permutation of n points whose cycle lengths are at least 3.

a(n) <= 12. - David A. Corneth, Jan 09 2022

The sequence is periodic with period 4620 = 3*4*5*7*11. If n is divisible by 3, 4, 5, 7 or 11 then a(n) is the smallest such divisor. Otherwise, a(n) = 12 since every number >= 6 has a partition into parts of size 3 and 4. - Andrew Howroyd, Jan 12 2022

Links

Table of n, a(n) for n=3..80.

Formula

a(3*k) = 3, a(12*k + 4) = a(12*k + 8) = 4, k >= 1. - David A. Corneth, Jan 09 2022

Example

a(13) = lcm(3,3,3,4) = 12.
a(14) = lcm(7,7) = 7.

Prog

(PARI) a(n)={my(m=oo); if(n>=3, forpart(p=n, m=min(m, lcm(Vec(p))), [3, n])); m} \\ Andrew Howroyd, Jan 09 2022
(PARI) a(n)={if(n<3, oo, for(k=3, 11, if(n%k==0, return(k))); 12)} \\ Andrew Howroyd, Jan 09 2022

Crossrefs

Sequence in context: A276737 A270027 A271726 * A354932 A123901 A349164

Adjacent sequences: A350637 A350638 A350639 * A350641 A350642 A350643

Keyword

easy,nonn

Author

Janaka Rodrigo, Jan 09 2022

Extensions

Terms corrected by Andrew Howroyd, Jan 09 2022

Status

approved