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A127481 Triangle T(n,k) read by rows: T(n,k) = sum_{l=k..n, l|n, k|l} l*phi(k). 2
1, 3, 2, 4, 0, 6, 7, 6, 0, 8, 6, 0, 0, 0, 20, 12, 8, 18, 0, 0, 12, 8, 0, 0, 0, 0, 0, 42, 15, 14, 0, 24, 0, 0, 0, 32, 13, 0, 24, 0, 0, 0, 0, 0, 54, 18, 12, 0, 0, 60, 0, 0, 0, 0, 40, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 110, 28, 24, 42, 32, 0, 36, 0, 0, 0, 0, 0, 48, 14, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..87.

FORMULA

T(n,1) = A000203(n).

T(n,n) = A002618(n).

T(n,k) =sum_{l=k..n} A127093(n,l) * A054522(l,k), the matrix product of the infinite lower triangular matrices.

EXAMPLE

First few rows of the triangle are:

1;

3, 2;

4, 0, 6;

7, 6, 0, 8;

6, 0, 0, 0, 20,

12, 8, 18, 0, 0, 12;

8, 0, 0, 0, 0, 0, 42;

15, 14, 0, 24, 0, 0, 0, 32;

...

MAPLE

A127481 := proc(n, k)

    a :=0 ;

    for l from k to n do

        if modp(n, l) =0 and modp(l, k) =0 then

            a := a+l*numtheory[phi](k) ;

        end if;

    end do:

    a ;

end proc: # R. J. Mathar, Sep 06 2013

CROSSREFS

Cf. A054522, A127093, A001157 (row sums), A002618, A127466.

Sequence in context: A129237 A127099 A004545 * A284552 A154879 A097673

Adjacent sequences:  A127478 A127479 A127480 * A127482 A127483 A127484

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Jan 15 2007

STATUS

approved

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Last modified April 22 04:04 EDT 2019. Contains 322329 sequences. (Running on oeis4.)