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Minimal values of m associated with A135061.
2

%I #13 Jul 23 2020 05:02:43

%S 1,3,4,6,9,13,15,19,23,28,36,37,44,50,52,57,63,73,78,87,90,96,104,109,

%T 115,123,133,139,147,157,162,169,178,189,195,202,212,224,230,251,248,

%U 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

%N Minimal values of m associated with A135061.

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

%H Robert Israel, <a href="/A135072/b135072.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%p f:= proc(n) local t; t:= floor(2*n^(3/2))+1; 1 + floor((t-sqrt(t^2-4*n^3))/2) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Mar 06 2017

%t a[n_] := With[{t = Floor[2n^(3/2)]+1}, 1 + Floor[(t-Sqrt[t^2-4n^3])/2]];

%t Array[a, 100] (* _Jean-François Alcover_, Jul 23 2020, after Maple *)

%o (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; }

%Y Cf. A135061.

%K nonn

%O 1,2

%A _Alexander R. Povolotsky_, Feb 11 2008, Feb 15 2008

%E Corrected and more terms added by _Robert Israel_, Mar 06 2017