A265675 Number of smaller squarefree numbers that are coprime to the n-th squarefree number.

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

Offset: 1

Author

Reinhard Zumkeller, Dec 13 2015

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A005117, A008966.

Programs

Haskell

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

Mathematica

With[{sf=Select[Range[200],SquareFreeQ]},Table[Total[Boole[CoprimeQ[sf[[n]],sf[[Range[1,n-1]]]]]],{n,70}]] (* Harvey P. Dale, Oct 12 2024 *)

Formula

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