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URL: https://oeis.org/A181832

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A181832
The product of the positive integers <= n that are strongly prime to n.
12
1, 1, 1, 1, 1, 3, 1, 20, 15, 35, 7, 36288, 35, 277200, 1485, 4576, 9009, 20432412000, 5005, 1097800704000, 459459, 5912192, 2834325, 2322315553259520000, 1616615, 124672148625024, 4865140665
OFFSET
0,6
COMMENTS
k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.
a(n) = A001783(n) / A007955(n-1) if n > 0 and a(0) = 1.
For 0 we have the empty product, giving 1. - Daniel Forgues, Aug 03 2012
From Robert G. Wilson v, Aug 04 2012: (Start)
Records appear at positions 0, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, ....
Except for 0 and 9, all records appear at prime positions and beginning with the sixth term, are == 0 (mod 100).
There are some primes which are not records: 2, 3, 61, 73, 109, 151, 181, 193, 229, 241, 271, 313, 349, 421, 433, 463, ....
Anti-records appear at positions 6, 10, 12, 14, 15, 18, 20, 24, 30, 36, 42, 48, 60, 66, 70, 78, 84, 90, 96, ..., and their values are odd. (End)
LINKS
Peter Luschny, Strong coprimality.
EXAMPLE
a(11) = 3 * 4 * 6 * 7 * 8 * 9 = 36288.
MAPLE
with(numtheory):
StrongCoprimes := n -> select(k->igcd(k, n)=1, {$1..n}) minus divisors(n-1):
A181832 := proc(n) local i; mul(i, i=StrongCoprimes(n)) end:
coprimorial := proc(n) local i; mul(i, i=select(k->igcd(k, n)=1, [$1..n])) end:
divisorial := proc(n) local i; mul(i, i=divisors(n)) end:
A181832a := n -> `if`(n=0, 1, coprimorial(n)/divisorial(n-1)):
MATHEMATICA
f[n_] := Times @@ Select[ Range@ n, GCD[#, n] == 1 && Mod[n - 1, #] != 0 &]; Array[f, 27, 0] (* Robert G. Wilson v, Aug 03 2012 *)
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 17 2010
STATUS
approved