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A247328
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Odd deficient numbers.
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4
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1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125
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OFFSET
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1,2
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COMMENTS
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Odd numbers n with sigma(n) < 2n.
945 is the first odd number that is not in the sequence.
Complement of A005231 (odd abundant numbers) with respect to A005408 (odd numbers), assuming that no odd perfect numbers exist. - Comment clarified by Daniel Forgues, Jan 19 2015
Complement of A125499 (even deficient numbers) with respect to A005100 (deficient numbers).
Asymptotically, among the deficient numbers, are there more evens than odds? - Daniel Forgues, Oct 24 2015
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LINKS
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Eric Weisstein's World of Mathematics, Abundance
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EXAMPLE
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27 is in the sequence because it is odd and its sum of divisors 1+3+9+27 is less than 2*27.
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MATHEMATICA
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a247328[n_Integer] :=
Select[Range[n], And[OddQ[#], DivisorSigma[1, #] < 2 #] &] (* Michael De Vlieger, Nov 08 2014 *)
Select[Range[1, 151, 2], DivisorSigma[1, #]<2 #&] (* Harvey P. Dale, Jun 22 2022 *)
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PROG
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(Magma) [n: n in [1..1000 by 2] | IsOdd(n) and SumOfDivisors(n) lt 2*n]
(PARI) select(n->(sigma(n)<2*n), vector(100, n, 2*n-1)) \\ Michel Marcus, Nov 06 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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