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A275257 Array read by upwards antidiagonals: LegendrePhi phi(x,n), x,n >=1.

%I A275257 #20 Jan 10 2018 14:22:53
%S A275257 1,2,1,3,1,1,4,2,2,1,5,2,2,1,1,6,3,3,2,2,1,7,3,4,2,3,1,1,8,4,4,3,4,1,
%T A275257 2,1,9,4,5,3,4,1,3,1,1,10,5,6,4,5,2,4,2,2,1,11,5,6,4,6,2,5,2,2,1,1,12,
%U A275257 6,7,5,7,3,6,3,3,2,2,1,13,6
%N A275257 Array read by upwards antidiagonals: LegendrePhi phi(x,n), x,n >=1.
%H A275257 Peter Kagey, <a href="/A275257/b275257.txt">Table of n, a(n) for n = 1..10000</a>
%H A275257 L. Toth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Toth2/toth5.html">On the Bi-Unitary Analogues of Euler's Arithmetical Function and the Gcd-Sum Function</a>, JIS 12 (2009) 09.5.2, function phi(x,n).
%F A275257 phi(x,n) = Sum_{k=1..x} A054431(k,n).
%F A275257 phi(n,n) = A000010(n).
%e A275257 Upper left corner of array begins
%e A275257    1 1 1 1 1 1 1 1 1 1 ...
%e A275257    2 1 2 1 2 1 2 1 2 1 ...
%e A275257    3 2 2 2 3 1 3 2 2 2 ...
%e A275257    4 2 3 2 4 1 4 2 3 2 ...
%e A275257    5 3 4 3 4 2 5 3 4 2 ...
%e A275257    6 3 4 3 5 2 6 3 4 2 ...
%e A275257    7 4 5 4 6 3 6 4 5 3 ...
%e A275257    8 4 6 4 7 3 7 4 6 3 ...
%e A275257    9 5 6 5 8 3 8 5 6 4 ...
%e A275257   10 5 7 5 8 3 9 5 7 4 ...
%p A275257 A275257 := proc(x,n)
%p A275257     local a,k ;
%p A275257     a :=0 ;
%p A275257     for k from 1 to x do
%p A275257         if igcd(k,n) = 1 then
%p A275257             a := a+1 ;
%p A275257         end if;
%p A275257     end do:
%p A275257     a ;
%p A275257 end proc:
%p A275257 seq(seq(A275257(d-n,n),n=1..d-1),d=2..15) ;
%t A275257 With[{nn = 14}, Table[#[[k, n - k + 1]], {n, nn - 1}, {k, n}] &@ Map[Accumulate, Table[Boole@ CoprimeQ[k, n], {n, nn}, {k, nn - n}]]] // Flatten (* _Michael De Vlieger_, Jan 09 2018 *)
%o A275257 (Ruby)
%o A275257 def a(x, n); (1..x).count { |k| k.gcd(n) == 1 } end
%o A275257 # _Peter Kagey_, Jan 08 2018
%Y A275257 Partial sums of A054431. Cf. A078401 (upper right triangle).
%K A275257 nonn,easy,tabl
%O A275257 1,2
%A A275257 _R. J. Mathar_, Jul 21 2016