A071318 Lesser of 2 consecutive numbers which are cubefree and not squarefree, i.e., numbers k such that both k and k+1 are in A067259.

44, 49, 75, 98, 99, 116, 147, 171, 244, 260, 275, 315, 332, 363, 387, 475, 476, 507, 524, 531, 548, 549, 603, 604, 636, 692, 724, 725, 747, 764, 774, 819, 844, 845, 846, 867, 908, 924, 931, 963, 980, 1035, 1075, 1083, 1179, 1196, 1251, 1274, 1275, 1324

Offset

1,1

Comments

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 5, 41, 407, 4125, 41215, 412331, 4123625, 41236308, ... . Apparently, the asymptotic density of this sequence exists and equals 0.041236... . - Amiram Eldar, Jan 18 2023

The asymptotic density of this sequence is Product_{p prime} (1 - 2/p^3) - 2 * Product_{p prime} (1 - 1/p^2 - 1/p^3) + Product_{p prime} (1 - 2/p^2) = 0.041236147082334172926... . - Amiram Eldar, Jan 05 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Formula

A051903(k) = A051903(k+1) = 2 when k is a term.

Example

75 is a term since 75 = 3*5^2 and 76 = 2^2*19.

Mathematica

With[{s = Select[Range[1350], And[MemberQ[#, 2], FreeQ[#, k_ /; k > 2]] &@ FactorInteger[#][[All, -1]] &]}, Function[t, Part[s, #] &@ Position[t, 1][[All, 1]]]@ Differences@ s] (* Michael De Vlieger, Jul 30 2017 *)

Prog

(Haskell)
a071318 n = a071318_list !! (n-1)
a071318_list = [x | x <- [1..],  a212793 x == 1, a008966 x == 0,
                    let y = x+1, a212793 y == 1, a008966 y == 0]
-- Reinhard Zumkeller, May 27 2012
(PARI) isok(n) = (n>1) && (vecmax(factor(n)[, 2])==2) && (vecmax(factor(n+1)[, 2])==2); \\ Michel Marcus, Aug 02 2017

Crossrefs

Subsequence of A067259, A340152.

Cf. A007674, A063528, A071619, A071620, A071621, A071622, A071623.

Cf. A008966, A051903, A212793.

Sequence in context: A365870 A088066 A116355 * A085651 A066124 A270298

Adjacent sequences: A071315 A071316 A071317 * A071319 A071320 A071321

Keyword

nonn

Author

Labos Elemer, May 29 2002

Status

approved