A214845 Triangle read by rows: T(n,m) =(n/k)^(k-1) mod k, where k is the m-th divisor of n, 1 <= m <= tau(n).

0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 3, 2, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 3, 4, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 4, 3, 8, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 3, 1, 2, 1, 0, 1, 0, 1, 1, 1, 5, 3, 4, 1

Offset: 1

Author

Gerasimov Sergey, Mar 08 2013

Keywords

• nonn
• tabf
• less

Comments

Row lengths are tau(n) = A000005(n).

The sequence of row sums starts: 0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 7, 1, 3, 3, 1, 1, 9, 1, 5, 3, 3, 1, 17, 1, 3, 1, 7, 1, 16, 1, 1, 3, 3, 3, 26, 1, 3, 3, 19, 1, 12, 1, 7, 18, 3, 1, 27, 1, 23...

Examples

			Triangle begins:
0;
0,1;
0,1;
0,0,1;
0,1;
0,1,1,1;
0,1;
0,0,0,1;
0,0,1;
0,1,1,1;
0,1;
0,0,1,3,2,1;
0,1;
0,1,1,1;
0,1,1,1;
0,0,0,0,1;
0,1;
0,1,0,3,4,1;
		

Crossrefs

Cf. A000005, A027750, A055225, A087909, A213919.

Programs

Maple

A214845 := proc(n,m)
    sort(convert(numtheory[divisors](n),list)) ;
    k := op(m,%) ;
    modp((n/k)^(k-1),k) ;
end proc:
for n from 1 to 30 do
    for m from 1 to numtheory[tau](n) do
        printf("%d,",A214845(n,m)) ;
    end do:
    printf("\n") ;
end do: # R. J. Mathar, Apr 17 2013