A171642 Non-deficient numbers with odd sigma such that the sum of the even divisors is twice the sum of the odd divisors.

18, 162, 450, 882, 1458, 2178, 2450, 3042, 4050, 5202, 6050, 6498, 7938, 8450, 9522, 11250, 13122, 15138, 17298, 19602, 22050, 24642, 27378, 30258, 33282, 36450, 39762, 43218, 46818, 50562, 54450, 58482, 61250, 62658, 66978, 71442, 76050, 80802, 85698

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

Cf. A000203, A023196, A074400, A000593.

Cf. A171641, A083207, A023196, A077591, A137933.

Sequence in context: A119004 A002698 A222914 * A158808 A271899 A128797

Adjacent sequences: A171639 A171640 A171641 * A171643 A171644 A171645

Keyword

nonn

Author

Peter Luschny, Dec 14 2009

Status

approved