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A181832
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The product of the positive integers <= n that are strongly prime to n.
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12
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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
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OFFSET
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0,6
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COMMENTS
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k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.
For 0 we have the empty product, giving 1. - Daniel Forgues, Aug 03 2012
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)
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LINKS
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EXAMPLE
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a(11) = 3 * 4 * 6 * 7 * 8 * 9 = 36288.
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MAPLE
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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)):
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MATHEMATICA
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f[n_] := Times @@ Select[ Range@ n, GCD[#, n] == 1 && Mod[n - 1, #] != 0 &]; Array[f, 27, 0] (* Robert G. Wilson v, Aug 03 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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