%I #4 Jun 10 2021 22:33:52

%S 1,28,176,561,2701,7381,29161,51681,115921,390241,260281,924001,

%T 1334161,1413721,1038961,3178981,8826301,3000025,16597441,33882241,

%U 12708361,22589281,31375081,63095761,90336961

%N a(n) is the least positive number k that can be written in exactly k ways as (x*y+1)*(x*z+1) with x > y > z > 1.

%C For n > 1, a(n) = A180045(k) where A332770(k) = n is the first appearance of n in A332770.

%e a(3) = 561 since 176 = (8*4+1)*(8*2+1) = (10*5+1)*(10*1+1) = (16*2+1)*(16*1+1) is the first number that can be obtained in exactly 3 ways.

%p N:= 10^8:

%p V:= Vector(N,datatype=integer[4]):

%p for x from 3 while (2*x+1)*(x+1) <= N do

%p for y from 2 to x-1 while (x*y+1)*(x+1) <= N do

%p for z from 1 to y-1 do

%p v:= (x*y+1)*(x*z+1);

%p if v > N then break fi;

%p V[v]:= V[v]+1;

%p od od od:

%p R:= Array(0..26):

%p for j from 1 to N do

%p v:= V[j]; if R[v] = 0 then R[v]:= j fi

%p od:

%p convert(R[0..24],list);

%Y Cf. A180045, A332770.

%K nonn

%O 0,2

%A _Robert Israel_, Jun 10 2021