A211487 Characteristic sequence of numbers n having a primitive root modulo n.

0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0

Offset

1

Comments

a(1) = 0, since we have an empty set of numbers more than 0 and less than 1.

If A(x) is the counting function of a(n)=1, n<=x, then A(x)~2*x/log(x) as x tends to infinity.

Characteristic function of A033948 (apart from the initial term). - Antti Karttunen, Aug 22 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = 1 iff n = 2, 4, p^k, 2*p^k, where p is an odd prime.

A001783(n) ≡ (-1)^a(n) mod n.

From Antti Karttunen, Aug 22 2017: (Start)

For n > 1, if A034380(n) = 1, a(n) = 1, otherwise a(n) = 0.

A103131(n) = (-1)^a(n) for n > 2.

(End)

Prog

(PARI) A211487(n) = if(n%2, !!isprimepower(n), (n==2 || n==4 || (isprimepower(n/2, &n) && n>2))); \\ Antti Karttunen, Aug 22 2017, after Charles R Greathouse IV's code for A033948.

Crossrefs

Cf. A001783, A033948, A034380, A103131.

Sequence in context: A075897 A135947 A360123 * A101040 A341591 A306453

Adjacent sequences: A211484 A211485 A211486 * A211488 A211489 A211490

Keyword

nonn

Author

Vladimir Shevelev, May 13 2012

Extensions

More terms from Antti Karttunen, Aug 22 2017

Status

approved