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A278115 Triangle T(n,k) = A278113(n,k)^2 A000040(k) for 1 <= k <= A278114(n), read by rows.

%I A278115 #16 Sep 08 2022 08:46:17
%S A278115 2,8,3,5,7,18,12,5,7,11,13,17,32,27,20,28,11,13,17,19,23,29,31,50,48,
%T A278115 45,28,44,13,17,19,23,29,31,37,41,43,47,72,48,45,63,44,52,68,19,23,29,
%U A278115 31,37,41,43,47,53,59,61,67,71,98,75,80,63,44,52,68,76,92,29,31,37,41,43,47,53
%N A278115 Triangle T(n,k) = A278113(n,k)^2 A000040(k) for 1 <= k <= A278114(n), read by rows.
%H A278115 Jason Kimberley, <a href="/A278115/b278115.txt">Table of i, a(i) for i = 1..10126 (T(n,k) for n = 1..46)</a>
%F A278115 T(n,k) = prime(k) * floor(n*sqrt(2/prime(k)))^2.
%e A278115 The first six rows are:
%e A278115 2;
%e A278115 8, 3, 5, 7;
%e A278115 18, 12, 5, 7, 11, 13, 17;
%e A278115 32, 27, 20, 28, 11, 13, 17, 19, 23, 29, 31;
%e A278115 50, 48, 45, 28, 44, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47;
%e A278115 72, 48, 45, 63, 44, 52, 68, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71;
%t A278115 Table[# Floor[n Sqrt[2/#]]^2 &@ Prime@ k, {n, 7}, {k, PrimePi[2 n^2]}] // Flatten (* _Michael De Vlieger_, Feb 17 2017 *)
%o A278115 (Magma)
%o A278115 A278112:=func<n,k|Isqrt(2*n^2 div k)>;
%o A278115 A278115_row:=func<n|[A278112(n,p)^2*p:p in PrimesUpTo(2*n^2)]>;
%o A278115 &cat[A278115_row(n):n in[1..7]];
%Y A278115 Cf. A278101.
%K A278115 nonn,tabf,easy
%O A278115 1,1
%A A278115 _Jason Kimberley_, Feb 10 2017