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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.
0
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
0,2
COMMENTS
For n > 1, a(n) = A180045(k) where A332770(k) = n is the first appearance of n in A332770.
EXAMPLE
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.
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);
CROSSREFS
Sequence in context: A366954 A129136 A042528 * A219821 A341160 A219386
KEYWORD
nonn
AUTHOR
Robert Israel, Jun 10 2021
STATUS
approved