A247328 Odd deficient numbers.

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

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 *)
Select[Range[1, 151, 2], DivisorSigma[1, #]<2 #&] (* Harvey P. Dale, Jun 22 2022 *)

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*n-1)) \\ Michel Marcus, Nov 06 2014

Crossrefs

Cf. A005100, A005231, A005408, A125499.

Sequence in context: A165747 A053229 A157142 * A317107 A317439 A004273

Adjacent sequences: A247325 A247326 A247327 * A247329 A247330 A247331

Keyword

nonn

Author

Jaroslav Krizek, Nov 05 2014

Status

approved