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

1,3

Links

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

Formula

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

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

Example

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;
...

Maple

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

Prog

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

Crossrefs

Cf. A000005, A130207, A130209.

Sequence in context: A242609 A226225 A329265 * A109127 A342721 A263456

Adjacent sequences: A130206 A130207 A130208 * A130210 A130211 A130212

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, May 16 2007

Extensions

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

Status

approved