A076144 Largest squarefree m <= sfn(n) such that m*sfn(n) is also squarefree, where sfn(n) is the n-th squarefree number.

1, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109

Offset: 1

Author

Reinhard Zumkeller, Oct 30 2002

Keywords

• nonn

Comments

gcd(a(n), spf(n)) = 1;

a(n+1) = sfn(n) for n < 106, but a(107) = 173 = sfn(105), as sfn(107)*sfn(106) = 177*174 = (3*59)*(2*3*29) is not squarefree.

The first n such that a(n+1) != A005117(n) (the squarefree integers) are 106, 258, 292, 368, 509, 515, 566, 653, 719, 807, 839, 882, 928, 992, .... - Emmanuel Vantieghem, Mar 10 2017

Links

• Emmanuel Vantieghem, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005117, A077395.

Programs

Mathematica

f[n_] := Module[{m = n}, While[! SquareFreeQ[m*n], m--]; m]; f /@ Select[ Range[110], SquareFreeQ] (* Amiram Eldar, Jul 07 2020 *)