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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 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.)