A073797 a(n) = 2^n mod pi(n).

0, 0, 0, 2, 1, 0, 0, 0, 0, 3, 1, 2, 4, 2, 4, 4, 1, 0, 0, 0, 0, 5, 1, 2, 4, 8, 7, 2, 4, 2, 4, 8, 5, 10, 9, 8, 4, 8, 4, 6, 12, 2, 4, 8, 2, 8, 1, 2, 4, 8, 1, 0, 0, 0, 0, 0, 0, 8, 16, 2, 4, 8, 16, 14, 10, 3, 6, 12, 5, 8, 16, 2, 4, 8, 16, 11, 1, 6, 12, 2, 4, 18, 13, 3, 6, 12, 1, 8, 16, 8, 16, 8, 16, 8, 16

Offset: 2

Author

Labos Elemer, Aug 12 2002

Keywords

• nonn

Examples

			From _Michael De Vlieger_, Dec 09 2018: (Start)
a(2) = 0 since 2^2 mod PrimePi(2) = 4 mod 1 = 0.
a(5) = 2 since 2^5 mod PrimePi(5) = 32 mod 3 = 2. (End)
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000079, A000720, A015910, A062173, A064367.

Programs

Magma

[2^n mod #PrimesUpTo(n): n in [2..100]]; // G. C. Greubel, Dec 10 2018

Mathematica

Array[Mod[2^#, PrimePi@ #] &, 95, 2] (* Michael De Vlieger, Dec 09 2018 *)
Table[PowerMod[2,n,PrimePi[n]],{n,2,100}] (* Harvey P. Dale, Aug 30 2021 *)

PARI

for(n=2, 100, print1(lift(Mod(2^n, primepi(n))), ", ")) \\ G. C. Greubel, Dec 10 2018

Sage

[mod(2^n, prime_pi(n)) for n in (2..100)] # G. C. Greubel, Dec 10 2018

Formula

a(n) = A000079(n) mod A000720(n).