A096459 - OEIS

%I #9 May 21 2017 07:31:37

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

%C T(n,k)=0 iff k is a prime factor of n:

%C A001221(n) = number of zeros in n-th row;

%C T(n,1)=A000035(n);

%C T(n,2)=A011655(n) for n>1; T(n,3)=A070430(n) for n>2;

%C T(n,4)=A053879(n) for n>3; T(n,5)=A070434(n) for n>4;

%C T(n,6)=A070436(n) for n>5; T(n,7)=A054580(n) for n>6;

%C T(n,8)=A070441(n) for n>7; T(n,9)=A070445(n) for n>8;

%C T(n,10)=A070451(n) for n>9;

%C T(n,n)=A069547(n).

%H G. C. Greubel, <a href="/A096459/b096459.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%e Triangle begins:

%e 1;

%e 0, 1;

%e 1, 0, 4;

%e 0, 1, 1, 2;

%e 1, 1, 0, 4, 3;

%e 0, 0, 1, 1, 3, 10;

%e 1, 1, 4, 0, 5, 10, 15;

%e ......

%t Table[Mod[n^2, Prime[k]], {n, 1, 10}, {k, 1, n}] (* _G. C. Greubel_, May 20 2017 *)

%Y Cf. A000290, A000040, A049759.

%K nonn,tabl

%O 1,6

%A _Reinhard Zumkeller_, Aug 12 2004