A278106 -id:A278106 - cp's OEIS frontend

A278102 a(n) is the largest j such that A278101(n,k) strictly decreases for k=1..j.

1, 2, 3, 2, 3, 4, 2, 4, 2, 3, 2, 3, 4, 2, 4, 2, 3, 2, 3, 4, 2, 5, 6, 5, 2, 2, 3, 2, 4, 4, 4, 2, 2, 3, 2, 3, 4, 4, 5, 2, 2, 2, 3, 5, 3, 5, 2, 2, 2, 3, 5, 2, 4, 4, 4, 2, 3, 4, 2, 4, 5, 4, 2, 3, 2, 2, 4, 5, 4, 3, 3, 2, 2, 3, 5, 4, 5, 2, 2, 2, 3, 2, 3, 4, 2, 2, 2, 3, 2, 3, 4, 6, 5, 2, 3, 2, 2, 4, 6, 6, 2, 3, 2

Offset: 1

Jason Kimberley, Nov 15 2016

Jason Kimberley, Table of n, a(n) for n = 1..10000

This is the row length sequence for triangles A278103 and A278104.

A278106 lists first occurrences in this sequence.

A277647:=func;
A278101_row:=funcA277647(n,k):k in[1..n^2]|IsSquarefree(k)]>;
A278102:=funcA278101_row(n) >;
[A278102(n):n in[1..103]];

Map[Length@ TakeWhile[FoldList[Function[s, Boole[s < 0] #2][#2 - #1] &, #], # > 0 &] &, #] &@ Map[DeleteCases[#, 0] &, Table[Boole[SquareFreeQ@ k] k Floor[n/Sqrt@ k]^2, {n, 23}, {k, n^2}] ] // Flatten (* Michael De Vlieger, Nov 24 2016 *)

A278119 a(n) is the index of the first occurrence of n in A278116.

Original entry on oeis.org

1, 2, 3, 5, 9, 27, 81, 163, 3451, 7372, 82177, 3716, 2769544, 25899347, 357567610, 4229297109

Offset: 1

Jason Kimberley, Feb 15 2017

a(18) = 42945966786, but a(17) > 5*10^10.

R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 106, Issue August 2018, p. 185-207.

Cf. A278106, A278116.

cp's OEIS Frontend

A278102 a(n) is the largest j such that A278101(n,k) strictly decreases for k=1..j.

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