A027435 Number of distinct products ij with 1 <= i <= n, 1 <= j <= n, (i,j)=1.

1, 2, 4, 6, 10, 11, 17, 21, 27, 29, 39, 42, 54, 57, 62, 70, 86, 89, 107, 113, 120, 125, 147, 152, 172, 178, 196, 204, 232, 236, 266, 282, 294, 302, 320, 329, 365, 374, 388, 400, 440, 446, 488, 501, 518, 529, 575, 586, 628, 638, 657, 672, 724, 733, 758, 778

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

S. W. Golomb, personal communication, Svalbard, Norway, 7/97.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000
• Harri Hakula, Pauliina Ilmonen, Vesa Kaarnioja, Computation of extremal eigenvalues of high-dimensional lattice-theoretic tensors via tensor-train decompositions, arXiv:1705.05163 [math.NA], 2017. See Table 2, d=4,5.

Crossrefs

Cf. A014665, A236309.

Programs

Maple

A027435 := proc(n)
    local L, i, j ;
    L := {};
    for i from 1 to n do
        for j from 1 to n do
            if igcd(i,j) = 1 then
            L := L union {i*j};
            end if;
        end do:
    end do:
    nops(L);
end proc:  # R. J. Mathar, Jun 09 2016

Mathematica

Array[-Boole[# > 1] + Length@ Union@ Apply[Join, Table[If[CoprimeQ @@ #, i j, 0] &@ {i, j}, {i, #}, {j, #}]] &, 56] (* Michael De Vlieger, Nov 01 2017 *)

PARI

a(n)={#Set(concat(vector(n, i, [i*j | j<-[1..n], gcd(i,j)==1])))} \\ Andrew Howroyd, Nov 15 2018

PARI

seq(n)={my(v=vector(n),t=1);for(n=1, n, t+=sum(i=1, n-1, gcd(i,n) == 1 && 0==sumdiv(i*n, d, my(t=i*n/d); gcd(t,d)==1 && dAndrew Howroyd, Nov 16 2018

Formula

a(n) = Sum_{k=1..n} A014665(n). - Sean A. Irvine, Nov 15 2018

For n>1: # of positive integers u <= n(n-1) such that p^H_p(u)<=n for all p<=u, where H_p(u) = highest power of p dividing u.

a(n) = A236309(n) + 1. - Andrew Howroyd, Nov 16 2018

Extensions

More terms from Olivier Gérard, Nov 15 1997