OFFSET
1,1
COMMENTS
Numbers which are non-deficient (2n <= sigma(n)) [A023196] such that sigma(n) [A000203] is odd and the sum of the even divisors [A074400] is twice the sum of the odd divisors [A000593].
The sequence of terms which are not of the form 72*k^2 + 72*k + 18 starts: 2450, 6050, 8450, 61250, 120050, 151250, 211250, 296450.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..1000
Peter Luschny, Zumkeller Numbers.
EXAMPLE
Example: divisors(18) = {1, 2, 3, 6, 9, 18}, sigma(18) = 39, and 2 + 6 + 18 = 2*(1 + 3 + 9).
MAPLE
with(numtheory): A171642 := proc(n) local k, s, a;
s := sigma(n); a := add(k, k=select(x->type(x, odd), divisors(n)));
if 3*a = s and 2*n <= s and type(s, odd) then n else NULL fi end:
PROG
(Python)
from sympy import divisors
A171642 = []
for n in range(1, 10**5):
....d = divisors(n)
....s = sum(d)
....if s % 2 and 2*n <= s and s == 3*sum([x for x in d if x % 2]):
........A171642.append(n)
# Chai Wah Wu, Aug 20 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 14 2009
STATUS
approved