A130208 Diagonalized matrix of A000203, sigma(n).

1, 0, 3, 0, 0, 4, 0, 0, 0, 7, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24

Offset

1,3

Comments

A130207 replaces sigma(n) with phi(n), A000010. A130209 replaces sigma(n) with d(n), A000005.

Links

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

Formula

Infinite lower triangular matrix with A000203, sigma(n), in the main diagonal and the rest zeros.

Example

First few rows of the triangle are:
1;
0, 3;
0, 0, 4;
0, 0, 0, 7;
0, 0, 0, 0, 6;
0, 0, 0, 0, 0, 12;
...

Prog

(PARI) for(n=1, 9, for(k=2, n, print1("0, ")); print1(sigma(n)", ")) \\ Charles R Greathouse IV, Feb 14 2013
(PARI) A130208(n) = if(ispolygonal(n, 3), sigma((sqrtint(1+(n*8))-1)/2), 0); \\ Antti Karttunen, Jan 17 2025

Crossrefs

Cf. A000203, A130207, A130209.

Sequence in context: A244126 A378039 A133109 * A363155 A364084 A288654

Adjacent sequences: A130205 A130206 A130207 * A130209 A130210 A130211

Keyword

nonn,tabl

Author

Gary W. Adamson, May 16 2007

Extensions

Data section extended up to a(120) by Antti Karttunen, Jan 17 2025

Status

approved