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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Aug 12 2004

Keywords

• nonn
• tabl

Comments

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

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

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

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

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

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

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

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

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

Examples

			Triangle begins:
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;
......
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A000290, A000040, A049759.

Programs

Mathematica

Table[Mod[n^2, Prime[k]], {n, 1, 10}, {k, 1, n}] (* G. C. Greubel, May 20 2017 *)