A265626 Let S be the set of factorizations of n! where the largest factor is the largest prime <= n, and let f(s) be the least factor in the factorization s. Then a(n) = max f(S).

2, 2, 2, 2, 3, 4, 3, 3, 4, 7, 6, 7, 7, 7, 7, 10, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 37, 37

Offset

2,1

Links

Table of n, a(n) for n=2..68.

Formula

a(n) > 5 for n > 10. a(n) < A007918(ceiling(A007917(n)/2)).

Example

2! = 2
3! = 2 * 3
4! = 2^3 * 3
5! = 2 * 3 * 4 * 5
6! = 3^2 * 4^2 * 5
7! = 4 * 5 * 6^2 * 7
8! = 3 * 4^3 * 5 * 6 * 7
9! = 3 * 4^2 * 5 * 6^3 * 7
10! = 4^2 * 5^2 * 6^4 * 7
11! = 7 * 8^2 * 9^2 * 10^2 * 11
12! = 6^5 * 7 * 8 * 10^2 * 11
13! = 7 * 8^2 * 9^2 * 10^2 * 11 * 12 * 13
14! = 7^2 * 8 * 9 * 10^2 * 11 * 12^3 * 13
15! = 7^2 * 9 * 10^3 * 11 * 12^4 * 13
16! = 7^2 * 10^3 * 11 * 12^6 * 13
17! = 10 * 11 * 12^4 * 13 * 14^2 * 15^2 * 16 * 17

Prog

(PARI) f(n, mn, mx)=if(n%mn, return(0)); n/=mn; if(n==1, return(1)); for(k=mn, mx, if(f(n, k, mx), return(1))); 0
a(n)=if(n<6, return(2)); my(p=precprime(n), q=nextprime(p/2), N=n!); forprime(r=q+1, p-1, N/=r^valuation(N, r)); forstep(k=q, 3, -1, if(f(N, k, p), return(k)))

Crossrefs

Cf. A001055, A007917, A007918, A076716, A177333.

Sequence in context: A119789 A025424 A216505 * A230230 A187821 A114775

Adjacent sequences: A265623 A265624 A265625 * A265627 A265628 A265629

Keyword

nonn

Author

Charles R Greathouse IV, Dec 10 2015

Status

approved