A354945 a(n) is the least k > 0 such that n is a non-isolated divisor of k!.

2, 2, 3, 4, 5, 5, 7, 6, 6, 6, 11, 11, 13, 7, 6, 6, 17, 17, 19, 7, 7, 11, 23, 10, 10, 13, 9, 9, 29, 29, 31, 11, 11, 17, 7, 7, 37, 19, 13, 13, 41, 41, 43, 11, 11, 23, 47, 14, 14, 14, 17, 17, 53, 11, 11, 11, 19, 29, 59, 59, 61, 31, 8, 8, 13, 13, 67, 23, 23, 23

Offset

1,1

Comments

A positive divisor d of m is non-isolated if either d-1 or d+1 also divides m.

For any v > 1, v appears A133951(v)-A133951(v-1) times.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

A002034(n) <= a(n) <= n for any n > 1.

a(p) = p for any prime number p.

a(n) = max(A002034(n), min(A002034(n-1), A002034(n+1))) for any n > 1.

Example

For n = 6:
- 6 divides 3!, but neither 5 nor 7 divide 3!,
- 6 divides 4!, but neither 5 nor 7 divide 4!,
- 6 divides 5!, and 5 divides 5!,
- so a(6) = 5.

Prog

(PARI) a(n) = my (f=1); for (k=2, oo, f*=k; if (f % (n*(n+1))==0, return (k), n>1 && f % (n*(n-1))==0, return (k)))

Crossrefs

Cf. A000142, A002034, A133951.

Sequence in context: A029070 A344672 A360141 * A112341 A242774 A183003

Adjacent sequences: A354942 A354943 A354944 * A354946 A354947 A354948

Keyword

nonn

Author

Rémy Sigrist, Jun 12 2022

Status

approved