A071623 -id:A071623 - cp's OEIS frontend

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

Labos Elemer, May 29 2002

nonn

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

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

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

Subsequence of A067259, A340152.
Cf. A007674, A063528, A071619, A071620, A071621, A071622, A071623.
Cf. A008966, A051903, A212793.

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

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 *)

isok(n) = (n>1) && (vecmax(factor(n)[, 2])==2) && (vecmax(factor(n+1)[, 2])==2); \\ Michel Marcus, Aug 02 2017

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

cp's OEIS Frontend

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.

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