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A096459 Triangle read by rows: T(n,k) = n^2 mod prime(k), 1<=k<=n.

%I A096459 #9 May 21 2017 07:31:37
%S A096459 1,0,1,1,0,4,0,1,1,2,1,1,0,4,3,0,0,1,1,3,10,1,1,4,0,5,10,15,0,1,4,1,9,
%T A096459 12,13,7,1,0,1,4,4,3,13,5,12,0,1,0,2,1,9,15,5,8,13,1,1,1,2,0,4,2,7,6,
%U A096459 5,28,0,0,4,4,1,1,8,11,6,28,20,33,1,1,4,1,4,0,16,17,8,24,14,21,5,0,1,1,0
%N A096459 Triangle read by rows: T(n,k) = n^2 mod prime(k), 1<=k<=n.
%C A096459 T(n,k)=0 iff k is a prime factor of n:
%C A096459 A001221(n) = number of zeros in n-th row;
%C A096459 T(n,1)=A000035(n);
%C A096459 T(n,2)=A011655(n) for n>1; T(n,3)=A070430(n) for n>2;
%C A096459 T(n,4)=A053879(n) for n>3; T(n,5)=A070434(n) for n>4;
%C A096459 T(n,6)=A070436(n) for n>5; T(n,7)=A054580(n) for n>6;
%C A096459 T(n,8)=A070441(n) for n>7; T(n,9)=A070445(n) for n>8;
%C A096459 T(n,10)=A070451(n) for n>9;
%C A096459 T(n,n)=A069547(n).
%H A096459 G. C. Greubel, <a href="/A096459/b096459.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%e A096459 Triangle begins:
%e A096459 1;
%e A096459 0, 1;
%e A096459 1, 0, 4;
%e A096459 0, 1, 1, 2;
%e A096459 1, 1, 0, 4, 3;
%e A096459 0, 0, 1, 1, 3, 10;
%e A096459 1, 1, 4, 0, 5, 10, 15;
%e A096459 ......
%t A096459 Table[Mod[n^2, Prime[k]], {n, 1, 10}, {k, 1, n}] (* _G. C. Greubel_, May 20 2017 *)
%Y A096459 Cf. A000290, A000040, A049759.
%K A096459 nonn,tabl
%O A096459 1,6
%A A096459 _Reinhard Zumkeller_, Aug 12 2004