

A247328


Odd deficient numbers.


4



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

1,2


COMMENTS

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


LINKS

Jaroslav Krizek, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Deficient Number
Eric Weisstein's World of Mathematics, Abundance
Wikipedia, Deficient number


EXAMPLE

27 is in the sequence because it is odd and its sum of divisors 1+3+9+27 is less than 2*27.


MATHEMATICA

a247328[n_Integer] :=
Select[Range[n], And[OddQ[#], DivisorSigma[1, #] < 2 #] &] (* Michael De Vlieger, Nov 08 2014 *)


PROG

(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*n1)) \\ Michel Marcus, Nov 06 2014


CROSSREFS

Cf. A000203, A005100, A005231, A005408, A125499.
Sequence in context: A165747 A053229 A157142 * A317107 A317439 A004273
Adjacent sequences: A247325 A247326 A247327 * A247329 A247330 A247331


KEYWORD

nonn,more


AUTHOR

Jaroslav Krizek, Nov 05 2014


STATUS

approved



