|
| |
|
|
A072513
|
|
Product of all n - d, where d < n and d is a divisor of n.
|
|
5
| |
|
|
1, 1, 2, 6, 4, 60, 6, 168, 48, 360, 10, 47520, 12, 1092, 1680, 20160, 16, 440640, 18, 820800, 5040, 4620, 22, 734469120, 480, 7800, 11232, 4953312, 28, 3946320000, 30, 9999360, 21120, 17952, 28560, 439723468800, 36, 25308, 35568, 35852544000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
FORMULA
| a(n) = (n-d_1)(n-d_2)...(n-d_k) where d_k is the largest divisor of n less than n (k = tau(n) - 1).
a(p) = p-1, a(pq) = pq(p-1)(q-1)(pq-1), p and q prime.
If n is not a prime or a prime square then n divides a(n).
|
|
|
EXAMPLE
| a(6) = (6-1)(6-2)(6-3) = 60.
For n = 16 the divisors d < n are 1,2,4 and 8, so a(16) = (16-1)*(16-2)*(16-4)*(16-8) = 15*14*12*8 = 20160.
|
|
|
PROG
| (PARI) for(n=1, 40, d=divisors(n); print1(prod(j=1, matsize(d)[2]-1, n-d[j]), ", "))
|
|
|
CROSSREFS
| Cf. A072512, A080497, A080498, A080500.
Sequence in context: A108435 A126262 A080499 * A022404 A118138 A004583
Adjacent sequences: A072510 A072511 A072512 * A072514 A072515 A072516
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 28 2002
|
|
|
EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 31 2002
|
| |
|
|
