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A127472 Triangle T(n,k) = Sum_{j=k..n, j|n, k|j} phi(j) read by rows, 1<=k<=n. 1
1, 2, 1, 3, 0, 2, 4, 3, 0, 2, 5, 0, 0, 0, 4, 6, 3, 4, 0, 0, 2, 7, 0, 0, 0, 0, 0, 6, 8, 7, 0, 6, 0, 0, 0, 4, 9, 0, 8, 0, 0, 0, 0, 0, 6, 10, 5, 0, 0, 8, 0, 0, 0, 0, 4, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 12, 9, 8, 6, 0, 6, 0, 0, 0, 0, 0, 4, 13 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Defined by the matrix product A054522 * A051731.

LINKS

Table of n, a(n) for n=1..79.

FORMULA

T(n,k) = Sum_{j=k..n} A054522(n,j) * A051731(j,k), 1<=k<=n.

EXAMPLE

First few rows of the triangle are;

.1;

.2, 1;

.3, 0, 2;

.4, 3, 0, 2;

.5, 0, 0, 0, 4;

.6, 3, 4, 0, 0, 2;

.7, 0, 0, 0, 0, 0, 6;

.8, 7, 0, 6, 0, 0, 0, 4;

....

MAPLE

A127472 := proc(n, k)

        a := 0 ;

        for j from k to n do

                if (n mod j = 0 ) and (j mod k =0 ) then

                        a := a+numtheory[phi](j) ;

                end if;

        end do;

        a ;

end proc:

seq(seq(A127472(n, k), k=1..n), n=1..14) ; # R. J. Mathar, Nov 11 2011

CROSSREFS

Cf. A054522, A051731, A062949 (row sums), A000010 (diagonal n=k), A127471 (swapped matrix product).

Sequence in context: A025642 A025643 A127478 * A194665 A004563 A329647

Adjacent sequences:  A127469 A127470 A127471 * A127473 A127474 A127475

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jan 15 2007

STATUS

approved

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)