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).
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
Offset: 1
Keywords
Examples
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.
Programs
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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; }
Comments