

A034258


Write n! as a product of n numbers, n! = k(1)*k(2)*...*k(n) with k(1) <= k(2) <= ..., in all possible ways; a(n) = max value of k(1).


3



1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 15, 15, 15, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22
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OFFSET

1,4


COMMENTS

36, 49, 52 and 55 are not in this sequence.  Don Reble, Nov 29 2001
a(n) >= a(n1).  Larry Reeves (larryr(AT)acm.org), Jan 06 2005
a(n) is a monotonic, though not strictly monotonic, increasing function of n.
Complement for 1st comment: a(124) = 35 and a(125) = 37 (see Guy's book). (End)


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B22, pp. 122123.


LINKS

Richard K. Guy and John L. Selfridge, Factoring factorial n, Amer. Math. Monthly, Vol. 105, No. 8 (1998), pp. 766767.


FORMULA



EXAMPLE

3! = 6 = 1*2*3 is the only possible factorization, so a(3) = 1.
27! = 8^4 * 9^6 * 10^6 * 11^2 * 12 * 13^2 * 14^3 * 17 * 19 * 23, with 4 + 6 + 6 + 2 + 1 + 2 + 3 + 1 + 1 + 1 = 27 factors, which is the required number. Since the first factor is 8, a(27) >= 8. In fact no larger value can be obtained and a(27) = 8.


CROSSREFS



KEYWORD

nonn,nice


AUTHOR



EXTENSIONS



STATUS

approved



