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A278117 Irregular triangle T(n,k) = A278115(n,k) for 1 <= k <= A278116(n), read by rows.

%I A278117 #11 Sep 08 2022 08:46:17
%S A278117 2,8,3,18,12,5,32,27,20,50,48,45,28,72,48,45,98,75,128,108,162,147,
%T A278117 125,112,99,200,192,180,175,242,192,180,175,288,243,338,300,392,363,
%U A278117 320,450,432,405,512,507,500,448,396,578,507,500,648,588,722,675,800,768,720
%N A278117 Irregular triangle T(n,k) = A278115(n,k) for 1 <= k <= A278116(n), read by rows.
%C A278117 Each row is the longest strictly decreasing prefix of the corresponding row of A278115.
%H A278117 Jason Kimberley, <a href="/A278117/b278117.txt">Table of i, a(i) for i = 1..10104 (T(n,k) for n = 1..3333)</a>
%e A278117 The first six rows are:
%e A278117 2;
%e A278117 8, 3;
%e A278117 18, 12, 5;
%e A278117 32, 27, 20;
%e A278117 50, 48, 45, 28;
%e A278117 72, 48, 45;
%t A278117 Map[Take[#, 1 + Length@ TakeWhile[Differences@ #, # < 0 &]] &, #] &@ Table[# Floor[n Sqrt[2/#]]^2 &@ Prime@ k, {n, 20}, {k, PrimePi[2 n^2]}] // Flatten (* _Michael De Vlieger_, Feb 17 2017 *)
%o A278117 (Magma)
%o A278117 A278112:=func<n,k|Isqrt(2*n^2 div k)>;
%o A278117 A278115_row:=func<n|[A278112(n,p)^2*p:p in PrimesUpTo(2*n^2)]>;
%o A278117 A278117_row:=func<n|(exists(dec){row[1..j]:j in[1..#row-1]|row[j]le row[j+1]}select dec else row) where row is A278115_row(n) >;
%o A278117 &cat[A278117_row(n):n in[1..20]];
%Y A278117 Cf. A278103, A278118.
%K A278117 nonn,tabf,easy
%O A278117 1,1
%A A278117 _Jason Kimberley_, Feb 12 2017