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

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, 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, 6, 7, 5, 7, 3, 6, 3, 3, 2, 2, 1, 13, 6

Offset: 1

Author

R. J. Mathar, Jul 21 2016

Keywords

• nonn
• easy
• tabl

Examples

			Upper left corner of array begins
   1 1 1 1 1 1 1 1 1 1 ...
   2 1 2 1 2 1 2 1 2 1 ...
   3 2 2 2 3 1 3 2 2 2 ...
   4 2 3 2 4 1 4 2 3 2 ...
   5 3 4 3 4 2 5 3 4 2 ...
   6 3 4 3 5 2 6 3 4 2 ...
   7 4 5 4 6 3 6 4 5 3 ...
   8 4 6 4 7 3 7 4 6 3 ...
   9 5 6 5 8 3 8 5 6 4 ...
  10 5 7 5 8 3 9 5 7 4 ...
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000
• L. Toth, On the Bi-Unitary Analogues of Euler's Arithmetical Function and the Gcd-Sum Function, JIS 12 (2009) 09.5.2, function phi(x,n).

Crossrefs

Partial sums of A054431. Cf. A078401 (upper right triangle).

Programs

Maple

A275257 := proc(x,n)
    local a,k ;
    a :=0 ;
    for k from 1 to x do
        if igcd(k,n) = 1 then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
seq(seq(A275257(d-n,n),n=1..d-1),d=2..15) ;

Mathematica

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 *)

Ruby

def a(x, n); (1..x).count { |k| k.gcd(n) == 1 } end
# Peter Kagey, Jan 08 2018

Formula

phi(x,n) = Sum_{k=1..x} A054431(k,n).

phi(n,n) = A000010(n).