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

1,6

Links

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

Formula

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

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

Example

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

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) ;

Prog

(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

Crossrefs

Cf. A000010, A130208, A130209.

Sequence in context: A070202 A280129 A227344 * A325433 A167688 A385379

Adjacent sequences: A130204 A130205 A130206 * A130208 A130209 A130210

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