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A354945
a(n) is the least k > 0 such that n is a non-isolated divisor of k!.
1
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
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 12 2022
STATUS
approved