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

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

Robert G. Wilson v, Table of n, a(n) for n = 0..1000

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 *)

Crossrefs

Cf. A181830, A181831, A181833, A181834, A181835, A181836, A001783, A007955.

Sequence in context: A038455 A343890 A067802 * A139723 A030042 A045496

Adjacent sequences: A181829 A181830 A181831 * A181833 A181834 A181835

Keyword

nonn

Author

Peter Luschny, Nov 17 2010

Status

approved