A345215 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.

1, 28, 176, 561, 2701, 7381, 29161, 51681, 115921, 390241, 260281, 924001, 1334161, 1413721, 1038961, 3178981, 8826301, 3000025, 16597441, 33882241, 12708361, 22589281, 31375081, 63095761, 90336961

Offset: 0

Author

Robert Israel, Jun 10 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A180045, A332770.

Programs

Maple

N:= 10^8:
V:= Vector(N,datatype=integer[4]):
for x from 3 while (2*x+1)*(x+1) <= N do
  for y from 2 to x-1 while (x*y+1)*(x+1) <= N do
    for z from 1 to y-1 do
      v:= (x*y+1)*(x*z+1);
      if v > N then break fi;
      V[v]:= V[v]+1;
od od od:
R:= Array(0..26):
for j from 1 to N do
  v:= V[j]; if R[v] = 0 then R[v]:= j fi
od:
convert(R[0..24],list);