%I #16 Sep 08 2022 08:46:17
%S 1,2,1,1,1,3,2,1,1,1,1,1,4,3,2,2,1,1,1,1,1,1,1,5,4,3,2,2,1,1,1,1,1,1,
%T 1,1,1,1,6,4,3,3,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,7,5,4,3,2,2,2,2,2,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,6,5,4,3,3,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1
%N Triangle T(n,k) = A278112(n,A000040(k)) for 1 <= k <= A278114(n), read by rows.
%C This triangle consists of those columns of A278112 that have prime index.
%H Jason Kimberley, <a href="/A278113/b278113.txt">Table of n, a(i) for i = 1..10126 (T(n,k) for n = 1..46</a>
%F T(n,k) = floor(n*sqrt(2/prime(k))).
%F T(n,k) sqrt(A000040(k)) <= n sqrt(2) < (T(n,k)+1) sqrt(A000040(k)).
%e The first eight rows are:
%e 1;
%e 2, 1, 1, 1;
%e 3, 2, 1, 1, 1, 1, 1;
%e 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1;
%e 5, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
%e 6, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
%e 7, 5, 4, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
%e 8, 6, 5, 4, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
%t Table[Floor[n Sqrt[2/Prime@ k]], {n, 8}, {k, PrimePi[2 n^2]}] // Flatten (* _Michael De Vlieger_, Feb 17 2017 *)
%o (Magma)
%o A278112:=func<n,k|Isqrt(2*n^2 div k)>;
%o A278113_row:=func<n|[A278112(n,p):p in PrimesUpTo(2*n^2)]>;
%o &cat[A278113_row(n):n in[1..8]];
%Y Cf. A000040, A277648, A278112, A278114, A278115, A278118.
%K nonn,tabf,easy
%O 1,2
%A _Jason Kimberley_, Feb 09 2017
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