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
Keywords
Examples
Divisors(18) = {1, 2, 3, 6, 9, 18}, sigma(18) = 39, and 2 + 6 + 18 = 2*(1 + 3 + 9).
Links
- Donovan Johnson, Table of n, a(n) for n = 1..1000
- Peter Luschny, Zumkeller Numbers.
Programs
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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:
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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
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