A104039 Number of primitive roots modulo prime(n)^2, where prime(n) is n-th prime.

1, 2, 8, 12, 40, 48, 128, 108, 220, 336, 240, 432, 640, 504, 1012, 1248, 1624, 960, 1320, 1680, 1728, 1872, 3280, 3520, 3072, 4000, 3264, 5512, 3888, 5376, 4536, 6240, 8704, 6072, 10656, 6000, 7488, 8748, 13612, 14448, 15664, 8640, 13680, 12288, 16464

Offset: 1

Author

Lekraj Beedassy, Mar 31 2005

Keywords

• nonn

References

• I. Niven, H. S. Zuckerman & H. L. Montgomery, An Introduction to the Theory of Numbers, 5th Ed., p. 102, John Wiley, NY, 1991.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[(NthPrime(n)-1)*EulerPhi((NthPrime(n)-1)): n in [1..50]]; // Vincenzo Librandi, Aug 18 2017

Maple

with(numtheory): for p from 1 to 100 do printf(`%d,`,(ithprime(p)-1)*phi(ithprime(p)-1)) od: # James Sellers, Apr 10 2005

Mathematica

Table[(Prime[n] - 1) EulerPhi[(Prime[n] - 1)], {n, 50}] (* Vincenzo Librandi, Aug 18 2017 *)

Formula

a(n) = (prime(n) - 1)*phi((prime(n) - 1)) = A006093(n)*A000010(A006093(n)) = A006093(n)*A008330(n).

Extensions

More terms from James Sellers, Apr 10 2005