OFFSET
1,4
COMMENTS
36, 49, 52 and 55 are not in this sequence. - Don Reble, Nov 29 2001
a(n) >= a(n-1). - Larry Reeves (larryr(AT)acm.org), Jan 06 2005
From Bernard Schott, Oct 31 2021: (Start)
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. 122-123.
LINKS
Diophante, A1987 - Les factorielles revisitées.
Richard K. Guy and John L. Selfridge, Factoring factorial n, Amer. Math. Monthly, Vol. 105, No. 8 (1998), pp. 766-767.
Bernard Schott, Corresponding products for n!
FORMULA
If p is prime, a(p-1) = a(p). - Bernard Schott, Oct 24 2021
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
More terms from Robert G. Wilson v, May 12 2001
Verified by Don Reble, Apr 22 2007
STATUS
approved