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

Author

Jaroslav Krizek, Nov 05 2014

Keywords

• nonn

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

Examples

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

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

Crossrefs

Cf. A005100, A005231, A005408, A125499.

Programs

Magma

[n: n in [1..1000 by 2] | IsOdd(n) and SumOfDivisors(n) lt 2*n]

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 *)

PARI

select(n->(sigma(n)<2*n), vector(100, n, 2*n-1)) \\ Michel Marcus, Nov 06 2014