OFFSET
1,1
COMMENTS
LINKS
Michael De Vlieger,Table of n, a(n) for n = 1..10000
FORMULA
Conjecture: a(n) = ((2*r) + 1)^2 * 2^(c+1) where r and c are the corresponding row and column of n in the table format ofA191432,where the first row and column are 0. -John Tyler Rascoe,Jul 12 2022
Sum_{n>=1} 1/a(n) = Pi^2/8 (A111003). -Amiram Eldar,Jul 09 2023
EXAMPLE
FromMichael De Vlieger,May 14 2017: (Start)
4 is a term since it is even and the sum of its divisors {1,2,4} = 7 - 2(4) = -1 is odd. It is an even square.
18 is a term since it is even and the sum of its divisors {1,2,3,6,9,18} = 39 - 2(18) = 3 is odd. It is 2 times a square, i.e., 2(9). (End)
MATHEMATICA
Do[s=DivisorSigma[1, n]-2*n; If[OddQ[s]&&!OddQ[n], Print[{n, s}]], {n, 1, 1000}]
(* Second program: *)
Select[Range[2, 2000, 2], OddQ[DivisorSigma[1, #] - 2 #] &] (*Michael De Vlieger,May 14 2017 *)
PROG
(Python)
from itertools import count, islice
from sympy.ntheory.primetest import is_square
defA088827_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda n:is_square(n) or is_square(n>>1), count(max(startvalue+(startvalue&1), 2), 2))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer,Oct 28 2003
STATUS
approved