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A275257
Array read by upwards antidiagonals: LegendrePhi phi(x,n), x,n >=1.
3
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
1,2
FORMULA
phi(x,n) = Sum_{k=1..x} A054431(k,n).
phi(n,n) = A000010(n).
EXAMPLE
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 ...
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 *)
PROG
(Ruby)
def a(x, n); (1..x).count { |k| k.gcd(n) == 1 } end
# Peter Kagey, Jan 08 2018
CROSSREFS
Partial sums of A054431. Cf. A078401 (upper right triangle).
Sequence in context: A138151 A207378 A166556 * A325027 A306735 A275937
KEYWORD
nonn,easy,tabl
AUTHOR
R. J. Mathar, Jul 21 2016
STATUS
approved