A265675 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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

LINKS

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

FORMULA

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

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 *)

PROG

(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

CROSSREFS

Cf. A005117, A008966.

Sequence in context: A335285 A336268 A075105 * A094020 A165609 A358462

Adjacent sequences: A265672 A265673 A265674 * A265676 A265677 A265678

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 13 2015

STATUS

approved