A135072 Minimal values of m associated with A135061.

1, 3, 4, 6, 9, 13, 15, 19, 23, 28, 36, 37, 44, 50, 52, 57, 63, 73, 78, 87, 90, 96, 104, 109, 115, 123, 133, 139, 147, 157, 162, 169, 178, 189, 195, 202, 212, 224, 230, 251, 248, 260, 278, 284, 294, 310, 309, 316, 325, 337, 351, 371, 376, 385, 399, 401, 419, 427, 437, 451, 469, 472, 480, 490, 503, 519

Offset

1,2

Comments

a(n) is the least m > 0 such that floor(n^3/m) + m = A135061(n). - Robert Israel, Mar 06 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

If t = floor(2*n^(3/2))+1, then a(n) = 1 + floor((t-sqrt(t^2-4*n^3))/2). - Robert Israel, Mar 06 2017

Maple

f:= proc(n) local t; t:= floor(2*n^(3/2))+1; 1 + floor((t-sqrt(t^2-4*n^3))/2) end proc:
map(f, [$1..100]); # Robert Israel, Mar 06 2017

Mathematica

a[n_] := With[{t = Floor[2n^(3/2)]+1}, 1 + Floor[(t-Sqrt[t^2-4n^3])/2]];
Array[a, 100] (* Jean-François Alcover, Jul 23 2020, after Maple *)

Prog

(PARI) a(n) = {local( minsum=0, cursum =0, minm=0, lastminsum=0); minsum = n^3 + 1; lastminsum= n^3 + 1; minm =1; for(m=1, n^3, cursum = floor(n^3/m + m); lastminsum = minsum; if(cursum < minsum, minsum = cursum); if(cursum < lastminsum, minm=m); ); minm; }

Crossrefs

Cf. A135061.

Sequence in context: A096846 A140570 A285303 * A375198 A032720 A289117

Adjacent sequences: A135069 A135070 A135071 * A135073 A135074 A135075

Keyword

nonn

Author

Alexander R. Povolotsky, Feb 11 2008, Feb 15 2008

Extensions

Corrected and more terms added by Robert Israel, Mar 06 2017

Status

approved