A130209 Diagonalized matrix of d(n), A000005, number of divisors of n.

1, 0, 2, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4

Offset: 1

Author

Gary W. Adamson, May 16 2007

Keywords

• nonn
• tabl
• easy

Examples

			First few rows of the triangle are:
1;
0, 2;
0, 0, 2;
0, 0, 0, 3;
0, 0, 0, 0, 2;
0, 0, 0, 0, 0, 4;
...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 rows of the triangle

Crossrefs

Cf. A000005, A130207, A130209.

Programs

Maple

A130209 := proc(n,k)
    if k = n then
        numtheory[tau](n);
    else
        0;
    end if;
end proc: # R. J. Mathar, Aug 06 2016

PARI

A130209(n) = if(ispolygonal(n,3), numdiv((sqrtint(1+(n*8))-1)/2), 0); \\ Antti Karttunen, Jan 17 2025

Formula

T(n,n) = A000005(n),

T(n,k) = 0 if n <> k.

Extensions

Data section extended up to a(105) by Antti Karttunen, Jan 17 2025