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A352612 (n-1)*prod(-p^2 where 2 <= p <= n-2 is prime and relatively prime to n)*prod(k where both k and (n-k) are composite and relatively prime to n) (mod n). 1
0, 1, 2, 3, 4, 5, 4, 7, 4, 9, 10, 11, 4, 9, 11, 1, 16, 17, 4, 1, 17, 17, 22, 23, 4, 1, 26, 1, 28, 29, 4, 17, 29, 25, 1, 25, 36, 11, 35, 39, 40, 25, 4, 7, 41, 27, 46, 23, 4, 31, 1, 23, 52, 1, 51, 55, 1, 49, 58, 1, 4, 37, 59, 55, 1, 49, 66, 33, 65, 31, 70, 25, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The convention for the empty product here is 1. The second product exists for all numbers greater than 210. See A141098.
Conjecture: For odd n, if a(n) == -1 (mod n) then n must be a prime power.
LINKS
EXAMPLE
For n=6 there are no prime totatives between 2 and 4 and there are also no composite totative pairs which add to 6 so both products do not exist and a(6)=n-1=5.
For n=25 these products exist and are given -44618574^2*12096 == 4 (mod 25). Therefore, a(25)=4.
PROG
(PARI) a(n)= {prod_p=1; prod_r=1; for(k=2, n-2, if(gcd(k, n)==1, if(isprime(k), prod_p=prod_p*k*(n-k); ); if(!isprime(k) && !isprime(n-k), prod_r=prod_r*k; ); ); ); (-prod_p*prod_r)%n; }
CROSSREFS
Sequence in context: A135680 A135682 A287415 * A083245 A111610 A119816
KEYWORD
nonn
AUTHOR
Craig J. Beisel, Mar 23 2022
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)