A064542 a(n) = Max { k | k! <= n! / k! } where m! = A000142(m), factorial.

1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 16, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41, 42, 43, 43

Offset

1,3

Comments

Also a(n) is a largest m such that m! <= sqrt(n!). - Zak Seidov, Jul 07 2009

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

n = 12: 5040 = 1*2*3*4*5*6*7 <= 8*9*10*11*12 = 95040 and as 40320 = 1*2*3*4*5*6*7*8 > 9*10*11*12 = 11880 we have a(12) = 7.

Prog

(PARI) { m=2; for (n=1, 1000, s=sqrt(n!); while (m! <= s, m++); write("b064542.txt", n, " ", m - 1) ) } \\ Harry J. Smith, Sep 18 2009

Crossrefs

Cf. A000142, A060048.

Sequence in context: A259549 A098295 A074840 * A210434 A256502 A177151

Adjacent sequences: A064539 A064540 A064541 * A064543 A064544 A064545

Keyword

nonn

Author

Reinhard Zumkeller, Oct 08 2001

Status

approved