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Irregular triangle read by rows: T(n,k) = floor(n/prime(k)^2) for 1 <= prime(k)^2 <= n.
3

%I #9 Sep 08 2022 08:46:17

%S 1,1,1,1,2,2,1,2,1,2,1,3,1,3,1,3,1,3,1,4,1,4,1,4,2,4,2,5,2,5,2,5,2,5,

%T 2,6,2,6,2,1,6,2,1,6,3,1,7,3,1,7,3,1,7,3,1,7,3,1,8,3,1,8,3,1,8,3,1,8,

%U 3,1,9,4,1,9,4,1,9,4,1,9,4,1,10,4,1,10,4,1,10,4,1,10,4,1,11,4,1,11,5,1

%N Irregular triangle read by rows: T(n,k) = floor(n/prime(k)^2) for 1 <= prime(k)^2 <= n.

%C This triangle consists of those columns of A278108 with prime index.

%C The row length sequence is A056811.

%H Jason Kimberley, <a href="/A278109/b278109.txt">Table of i, a(i) for i = 4..7656 (T(n,k) for n = 4..1000)</a>

%F T(n,k) = A278108(n,A000040(k)).

%e The initial rows (for n = 4..27) are:

%e 1;

%e 1;

%e 1;

%e 1;

%e 2;

%e 2, 1;

%e 2, 1;

%e 2, 1;

%e 3, 1;

%e 3, 1;

%e 3, 1;

%e 3, 1;

%e 4, 1;

%e 4, 1;

%e 4, 2;

%e 4, 2;

%e 5, 2;

%e 5, 2;

%e 5, 2;

%e 5, 2;

%e 6, 2;

%e 6, 2, 1;

%e 6, 2, 1;

%e 6, 3, 1;

%o (Magma) [n div p^2:p in PrimesUpTo(Isqrt(n)),n in[1..45]];

%Y Cf. A056811, A277648, A278108, A278110.

%K nonn,easy,tabf

%O 4,5

%A _Jason Kimberley_, Feb 02 2017