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

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, 45, 28, 44, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 72, 48, 45, 63, 44, 52, 68, 19, 23, 29, 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

Offset

1,1

Links

Jason Kimberley, Table of i, a(i) for i = 1..10126 (T(n,k) for n = 1..46)

Formula

T(n,k) = prime(k) * floor(n*sqrt(2/prime(k)))^2.

Example

The first six rows are:
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, 45, 28, 44, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47;
72, 48, 45, 63, 44, 52, 68, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71;

Mathematica

Table[# Floor[n Sqrt[2/#]]^2 &@ Prime@ k, {n, 7}, {k, PrimePi[2 n^2]}] // Flatten (* Michael De Vlieger, Feb 17 2017 *)

Prog

(Magma)
A278112:=func<n, k|Isqrt(2*n^2 div k)>;
A278115_row:=func<n|[A278112(n, p)^2*p:p in PrimesUpTo(2*n^2)]>;
&cat[A278115_row(n):n in[1..7]];

Crossrefs

Cf. A278101.

Sequence in context: A011431 A243340 A173823 * A222296 A258223 A154928

Adjacent sequences: A278112 A278113 A278114 * A278116 A278117 A278118

Keyword

nonn,tabf,easy

Author

Jason Kimberley, Feb 10 2017

Status

approved