cp's OEIS Frontend

A181832 The product of the positive integers <= n that are strongly prime to n.

%I A181832 #31 Mar 23 2016 09:04:26
%S A181832 1,1,1,1,1,3,1,20,15,35,7,36288,35,277200,1485,4576,9009,20432412000,
%T A181832 5005,1097800704000,459459,5912192,2834325,2322315553259520000,
%U A181832 1616615,124672148625024,4865140665
%N A181832 The product of the positive integers <= n that are strongly prime to n.
%C A181832 k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.
%C A181832 a(n) = A001783(n) / A007955(n-1) if n > 0 and a(0) = 1.
%C A181832 For 0 we have the empty product, giving 1. - _Daniel Forgues_, Aug 03 2012
%C A181832 From _Robert G. Wilson v_, Aug 04 2012: (Start)
%C A181832 Records appear at positions 0, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, ....
%C A181832 Except for 0 and 9, all records appear at prime positions and beginning with the sixth term, are == 0 (mod 100).
%C A181832 There are some primes which are not records: 2, 3, 61, 73, 109, 151, 181, 193, 229, 241, 271, 313, 349, 421, 433, 463, ....
%C A181832 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)
%H A181832 Robert G. Wilson v, <a href="/A181832/b181832.txt">Table of n, a(n) for n = 0..1000</a>
%H A181832 Peter Luschny, <a href="http://www.oeis.org/wiki/User:Peter_Luschny/StrongCoprimality">Strong coprimality</a>.
%e A181832 a(11) = 3 * 4 * 6 * 7 * 8 * 9 = 36288.
%p A181832 with(numtheory):
%p A181832 StrongCoprimes := n -> select(k->igcd(k,n)=1,{$1..n}) minus divisors(n-1):
%p A181832 A181832 := proc(n) local i; mul(i,i=StrongCoprimes(n)) end:
%p A181832 coprimorial := proc(n) local i; mul(i,i=select(k->igcd(k,n)=1,[$1..n])) end:
%p A181832 divisorial  := proc(n) local i; mul(i,i=divisors(n)) end:
%p A181832 A181832a := n -> `if`(n=0,1,coprimorial(n)/divisorial(n-1)):
%t A181832 f[n_] := Times @@ Select[ Range@ n, GCD[#, n] == 1 && Mod[n - 1, #] != 0 &]; Array[f, 27, 0] (* _Robert G. Wilson v_, Aug 03 2012 *)
%Y A181832 Cf. A181830, A181831, A181833, A181834, A181835, A181836, A001783, A007955.
%K A181832 nonn
%O A181832 0,6
%A A181832 _Peter Luschny_, Nov 17 2010