|
Search: id:A138196
|
|
|
| A138196 |
|
Number of different ways n! can be represented as the difference of two squares; also, for n>=4, half the number of positive integer divisors of n!/4. |
|
+0
1
|
|
| 1, 0, 0, 2, 4, 9, 18, 36, 60, 105, 210, 324, 648, 1080, 1680, 2352, 4704, 6480, 12960, 18360, 27200, 43200, 86400, 110880, 155232, 243936, 310464, 423360, 846720, 1080000, 2160000, 2592000, 3686400, 5713920, 7713792, 9237888, 18475776
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
FORMULA
|
For n>=4, if p(i) is the i-th prime (i.e. p(1)=2, p(2)=3, p(3)=5, etc.), with p(k) the largest prime not exceeding n, and n!/4 = (p(1)^e(1))*(p(2)^e(2))* ... *(p(k)^e(K)), then a(n) = (1/2)*(e(1)+1)*(e(2)+1)* ... *(e(k)+1).
|
|
EXAMPLE
|
a(5)=4 since 5! = 120 = 31^2-29^2 = 17^2-13^2 = 13^2-7^2 = 11^2-1^2.
|
|
CROSSREFS
|
Adjacent sequences: A138193 A138194 A138195 this_sequence A138197 A138198 A138199
Sequence in context: A065055 A065030 A103321 this_sequence A101351 A111662 A119027
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
John T. Robinson (jrobinson(AT)acm.org), May 04 2008
|
|
|
Search completed in 0.002 seconds
|
