OFFSET
1,1
COMMENTS
Is it possible to find a closed form formula for this sequence?
Numbers k such that 6*k+1 has at least 5 divisors == 1 (mod 6). - Robert Israel, Jan 20 2019
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
106 is in this sequence because 106 can be expressed in two different ways as 6xy + x + y: 6*8*2 + 8 + 2 and 6*15*1 + 15 + 1.
MAPLE
filter:= proc(n) nops(select(t -> t mod 6 =1, numtheory:-divisors(6*n+1)))>= 5 end proc:
select(filter, [$1..2000]); # Robert Israel, Jan 20 2019
MATHEMATICA
Select[Range[1329], 2 == Length@ FindInstance[ 6*x*y+x+y == # && x >= y > 0, {x, y}, Integers, 2] &] (* Giovanni Resta, May 29 2018 *)
PROG
(Python)
# Finding duplicates in matrix A where {a_ij}=6*i*j+i+j
def cuenta(a):
repa=[]
dupo=[]
k=0
sumo=0
while k<len(a)-1:
j=k+1
dupa = 1
while j<len(a) and a[j]==a[k]:
dupa +=1
j+=1
if dupa>1:
repa.append(a[k])
dupo.append(dupa)
sumo +=(dupa-1)
k +=dupa
return repa, dupo, sumo
kuno = []
for k in range(1, a + 1):
for j in range(1, k + 1):
m=6 * k * j + k + j
if m <= NN // 6: kuno.append(m)
kuno=sorted(kuno)
repkuno, dupkuno, suno= cuenta(kuno)
print(repkuno)
#
#END
(PARI) is(n) = my(i=0); for(x=1, n, for(y=1, x, if(n==6*x*y+x+y, i++; if(i==2, return(1))))); 0 \\ Felix Fröhlich, May 29 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Pedro Caceres, May 22 2018
STATUS
approved