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

1,3

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

Mathematica

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

Crossrefs

Cf. A005117, A077395.

Sequence in context: A348961 A367801 A348506 * A005117 A144338 A077377

Adjacent sequences: A076141 A076142 A076143 * A076145 A076146 A076147

Keyword

nonn

Author

Reinhard Zumkeller, Oct 30 2002

Status

approved