A236309 -id:A236309 - cp's OEIS frontend

A014665 Number of new fractions m/n < 1, where (m,n)=1 and "new" means the value of m*n has not occurred before.

1, 1, 2, 2, 4, 1, 6, 4, 6, 2, 10, 3, 12, 3, 5, 8, 16, 3, 18, 6, 7, 5, 22, 5, 20, 6, 18, 8, 28, 4, 30, 16, 12, 8, 18, 9, 36, 9, 14, 12, 40, 6, 42, 13, 17, 11, 46, 11, 42, 10, 19, 15, 52, 9, 25, 20, 21, 14, 58, 10, 60, 15, 28, 32, 29, 9, 66, 21, 26, 11, 70, 20, 72, 18, 23, 23, 42, 11, 78, 23, 54

Offset: 1

N. J. A. Sloane

nonn

			{1}, {1/2}, {1/3,2/3}, {1/4,3/4}, {1/5,...,4/5}, {5/6}, ...

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

Andrew Howroyd, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe).

Cf. A027435, A236309.

a[1] = 1;
a[n_] := Sum[Boole[GCD[i, n] == 1 && Sum[t = i*n/d; Boole[GCD[t, d] == 1 && t < d < n], {d, Divisors[i*n]}] == 0], {i, 1, n - 1}];
Array[a, 100] (* Jean-François Alcover, Sep 05 2019, from PARI *)

a(n)=if(n==1, 1, 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

Example corrected by and more terms from Olivier Gérard, Feb 1999

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

Original entry on oeis.org

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

N. J. A. Sloane

nonn

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

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.

Cf. A014665, A236309.

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

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

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

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

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

More terms from Olivier Gérard, Nov 15 1997

cp's OEIS Frontend

A014665 Number of new fractions m/n < 1, where (m,n)=1 and "new" means the value of m*n has not occurred before.

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

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