A130207 Diagonalized matrix of A000010, Euler totient function phi.

1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6

Offset: 1

Author

Gary W. Adamson, May 16 2007

Keywords

• nonn
• tabl
• easy

Examples

			First few rows of the triangle are:
1;
0, 1;
0, 0, 2;
0, 0, 0, 2;
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. A000010, A130208, A130209.

Programs

Maple

A130207 := proc(n,k)
    if k = n then
        numtheory[phi](n);
    else
        0;
    end if;
end proc:
seq(seq(A130207(n,k),k=1..n),n=1..15) ;

PARI

for(n=1,9,for(k=2,n,print1("0, "));print1(eulerphi(n)", ")) \\ Charles R Greathouse IV, Feb 19 2013

PARI

A130207(n) = if(ispolygonal(n,3), eulerphi((sqrtint(1+(n*8))-1)/2), 0); \\ Antti Karttunen, Jan 17 2025

Formula

T(n,n) = A000010(n).

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

Extensions

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