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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)