A078401 -id:A078401 - cp's OEIS frontend

A092790 a(n) = (n+1)*phi(n-1)/2.

2, 5, 6, 14, 8, 27, 20, 33, 24, 65, 28, 90, 48, 68, 72, 152, 60, 189, 88, 138, 120, 275, 104, 270, 168, 261, 180, 434, 128, 495, 272, 350, 288, 444, 228, 702, 360, 492, 336, 860, 264, 945, 460, 564, 528, 1127, 400, 1071, 520, 848, 648, 1430, 504, 1140, 696, 1062, 840, 1769

Offset: 3

N. J. A. Sloane, Nov 04 2008

[The old entry with this sequence number was a duplicate of A082470.]
Prepending [0, 3] and setting offset = 0 the sequence becomes the row sums of A378068. - Peter Luschny, Dec 27 2024
a(n) is the sum of row n-1 of A078401. - Amiram Eldar, May 12 2025

Amiram Eldar, Table of n, a(n) for n = 3..10000
Jeffrey Jaffe, Permutation numbers, Math. Mag., 49 (1976), 80-84.

Cf. A000010 (phi), A078401, A378068.

Table[(n+1) EulerPhi[n-1]/2,{n,3,60}] (* Harvey P. Dale, Apr 22 2012 *)

a(n) = (n+1)*eulerphi(n-1)/2; \\ Michel Marcus, Sep 18 2017

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

Original entry on oeis.org

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

R. J. Mathar, Jul 21 2016

			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 ...

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).

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

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) ;

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 *)

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

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

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

cp's OEIS Frontend

A092790 a(n) = (n+1)*phi(n-1)/2.

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

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