|
|
A027435
|
|
Number of distinct products ij with 1 <= i <= n, 1 <= j <= n, (i,j)=1.
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
S. W. Golomb, personal communication, Svalbard, Norway, 7/97.
|
|
LINKS
|
|
|
FORMULA
|
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.
|
|
MAPLE
|
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);
|
|
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 *)
|
|
PROG
|
(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 && d<n && t<d)); v[n]=t); v} \\ Andrew Howroyd, Nov 16 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|