A079709 Numbers m such that the squarefree kernel of m is less than the squarefree kernel of m+1.

1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 18, 20, 21, 22, 25, 27, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 41, 42, 45, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 61, 64, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 78, 81, 82, 84, 85, 86, 88, 90, 92, 93, 94, 96, 98, 100, 101, 102, 104, 105

Offset

1,2

Comments

The numbers of terms not exceeding 10^k for k = 1, 2, ... are 8, 67, 655, 6607, 66090, 661270, 6612947, 66131281, 661316300, 6613168473, ... Apparently the asymptotic density of this sequence is 0.66131... - Amiram Eldar, Aug 31 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) is asymptotic to c*n where c=1.51...

Mathematica

rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; Select[Range[100], rad[#] < rad[# + 1] &] (* Amiram Eldar, Aug 31 2020 *)

Crossrefs

Complement of A079710.

Cf. A007947 (squarefree kernel).

Sequence in context: A249245 A279607 A292636 * A285496 A247778 A003511

Adjacent sequences: A079706 A079707 A079708 * A079710 A079711 A079712

Keyword

nonn

Author

Benoit Cloitre, Jan 31 2003

Status

approved