

A270651


Triangular array: T(n,k) = greatest m such that 2^m divides prime(n)^2  prime(k)^2, where 3 <= k <= n.


2



4, 3, 3, 4, 5, 3, 5, 4, 3, 4, 3, 3, 4, 3, 3, 5, 4, 3, 4, 6, 3, 3, 3, 5, 3, 3, 4, 3, 6, 4, 3, 4, 5, 3, 5, 3, 3, 3, 4, 3, 3, 5, 3, 4, 3, 4, 6, 3, 5, 4, 3, 4, 3, 4, 3, 3, 3, 5, 3, 3, 4, 3, 7, 3, 4, 3, 4, 5, 3, 6, 4, 3, 4, 3, 4, 3, 5, 3, 3, 3, 4, 3, 3, 7, 3, 4, 3, 5, 3, 4, 3, 4, 5, 3, 7, 4, 3, 4, 3, 4, 3, 5, 3, 6, 3
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OFFSET

3,1


LINKS

Clark Kimberling, Table of n, a(n) for n = 3..10000


EXAMPLE

First 9 rows (n = 3 up to 11)::
4
3 3
4 5 3
5 4 3 4
3 3 4 3 3
5 4 3 4 6 3
3 3 5 3 3 4 3
6 4 3 4 5 3 5 3
3 3 4 3 3 5 3 4 3
For n = 5, the numbers p^2  q^2 are 121  9 = 16*7, 121  25 = 32*3, 121  49 = 8*7, so that row 3 (for n = 5) is (4, 5, 3).


MATHEMATICA

a[n_] := Table[IntegerExponent[Prime[n]^2  Prime[m]^2, 2], {m, 2, n  1}]
TableForm[Table[a[n], {n, 2, 16}]]
Flatten[Table[a[n], {n, 2, 16}]]


CROSSREFS

Cf. A000040, A270649.
Sequence in context: A303701 A179845 A180217 * A222635 A222649 A222616
Adjacent sequences: A270648 A270649 A270650 * A270652 A270653 A270654


KEYWORD

nonn,tabl,easy


AUTHOR

Clark Kimberling, Apr 26 2016


STATUS

approved



