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A171642 Non-deficient numbers with odd sigma such that the sum of the even divisors is twice the sum of the odd divisors. 1
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 (list; graph; refs; listen; history; text; internal format)
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 a(n) which have not the form 72n^2+72n+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. 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

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.