

A265675


Number of smaller squarefree numbers that are coprime to the nth squarefree number.


4



0, 1, 2, 3, 2, 5, 3, 7, 8, 5, 6, 11, 12, 8, 9, 15, 10, 17, 8, 19, 13, 13, 15, 23, 15, 17, 26, 11, 28, 18, 30, 21, 32, 25, 23, 23, 36, 37, 25, 30, 18, 41, 29, 22, 44, 45, 30, 36, 22, 49, 32, 51, 41, 34, 39, 55, 44, 41, 38, 47, 60, 61, 30, 63, 36, 43, 66, 67
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OFFSET

1,3


COMMENTS

a(n) = number of A005117(k) such that A005117(k) and A005117(n) are coprime, k = 1..n1.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = Sum_{k=1..n1} A008966(A005117(n)*A005117(k)).


EXAMPLE

A005117(7) = 10, A005117(1..6) = [1,2,3,5,6,7],
> a(7) = #{1,3,7} = 3;
A005117(8) = 11, A005117(1..7) = [1,2,3,5,6,7,10],
> a(8) = #{1,2,3,5,6,7,10} = 7;
A005117(9) = 13, A005117(1..8) = [1,2,3,5,6,7,10,11],
> a(9) = #{1,2,3,5,6,7,10,11} = 8;
A005117(10) = 14, A005117(1..9) = [1,2,3,5,6,7,10,11,13],
> a(10) = #{1,3,5,11,13} = 5;
A005117(11) = 15, A005117(1..10) = [1,2,3,5,6,7,10,11,13,14],
> a(11) = #{1,2,7,11,13,14} = 6.


PROG

(Haskell)
import Data.List (inits)
a265675 n = a265675_list !! (n1)
a265675_list = map (\(x:xs) > length $ filter ((== 1) . gcd x) xs) $
map reverse $ tail $ inits a005117_list


CROSSREFS

Cf. A005117, A008966.
Sequence in context: A335285 A336268 A075105 * A094020 A165609 A141465
Adjacent sequences: A265672 A265673 A265674 * A265676 A265677 A265678


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Dec 13 2015


STATUS

approved



