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Odd deficient numbers.
4

%I #35 Sep 08 2022 08:46:09

%S 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,

%T 49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,

%U 95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125

%N Odd deficient numbers.

%C Odd numbers n with sigma(n) < 2n.

%C 945 is the first odd number that is not in the sequence.

%C 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

%C Complement of A125499 (even deficient numbers) with respect to A005100 (deficient numbers).

%C Asymptotically, among the deficient numbers, are there more evens than odds? - _Daniel Forgues_, Oct 24 2015

%H Jaroslav Krizek, <a href="/A247328/b247328.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DeficientNumber.html">Deficient Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Abundance.html">Abundance</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Deficient_number">Deficient number</a>

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

%t a247328[n_Integer] :=

%t Select[Range[n], And[OddQ[#], DivisorSigma[1, #] < 2 #] &] (* _Michael De Vlieger_, Nov 08 2014 *)

%t Select[Range[1,151,2],DivisorSigma[1,#]<2 #&] (* _Harvey P. Dale_, Jun 22 2022 *)

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

%o (PARI) select(n->(sigma(n)<2*n), vector(100, n, 2*n-1)) \\ _Michel Marcus_, Nov 06 2014

%Y Cf. A005100, A005231, A005408, A125499.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Nov 05 2014