

A252649


The number of positive integers that are less than or equal to n that have a primitive root.


0



1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 15, 15, 15, 16, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 29, 29, 30, 31, 31, 31, 32, 33, 33, 33, 33, 34, 35, 35, 36, 37, 37, 37, 37, 37, 38, 38, 38, 38, 39, 39, 40, 41, 41, 41, 41, 41, 42, 42, 43, 44, 45, 45, 45, 46, 46, 46, 47, 47, 47, 47, 47, 48, 48, 48, 49, 50, 50, 50
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OFFSET

1,2


COMMENTS

Equivalently a(n) is the number of positive integers less than or equal to n that are 1,2,4 or of the form p^i or 2*p^i where p is an odd prime.
a(10^k) for k=1,2,...,7: 9, 50, 293, 1969, 14889, 120424, 1014032.


LINKS

Table of n, a(n) for n=1..100.
Eric Weisstein's World of Mathematics, Primitive Root


FORMULA

a(n) ~ 3/2 * n/log(n).  Vaclav Kotesovec, Dec 20 2014


EXAMPLE

a(12)=10 because there are 10 positive integers that are less than or equal to 12 that have a primitive root:1,2,3,4,5,6,7,9,10,11.


MATHEMATICA

Table[Length[Select[Range[2, n], IntegerQ[PrimitiveRoot[#]] &]] +
1, {n, 1, 100}]
Accumulate[Table[If[Length[PrimitiveRootList[n]]>0, 1, 0], {n, 100}]]+1 (* Harvey P. Dale, Jul 19 2019 *)


CROSSREFS

Cf. A033948.
Sequence in context: A100721 A271490 A265359 * A095703 A101041 A093697
Adjacent sequences: A252646 A252647 A252648 * A252650 A252651 A252652


KEYWORD

nonn


AUTHOR

Geoffrey Critzer, Dec 19 2014


STATUS

approved



