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A028983 Numbers whose sum of divisors is even. 33

%I

%S 3,5,6,7,10,11,12,13,14,15,17,19,20,21,22,23,24,26,27,28,29,30,31,33,

%T 34,35,37,38,39,40,41,42,43,44,45,46,47,48,51,52,53,54,55,56,57,58,59,

%U 60,61,62,63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,82

%N Numbers whose sum of divisors is even.

%C The even terms of this sequence are the even terms appearing in A178910. [Edited by _M. F. Hasler_, Oct 02 2014]

%C A071324(a(n)) is even. - _Reinhard Zumkeller_, Jul 03 2008

%C Sigma(a(n)) = A000203(a(n)) = A152678(n). - _Jaroslav Krizek_, Oct 06 2009

%C A083207 is a subsequence. - _Reinhard Zumkeller_, Jul 19 2010

%C Numbers k such that the number of odd divisors of k (A001227) is even. - _Omar E. Pol_, Apr 04 2016

%C Numbers k such that the sum of odd divisors of k (A000593) is even. - _Omar E. Pol_, Jul 05 2016

%C Numbers with a squarefree part greater than 2. - _Peter Munn_, Apr 26 2020

%C Equivalently, numbers whose odd part is nonsquare. Compare with the numbers whose square part is even (i.e., nonodd): these are the positive multiples of 4, A008586\{0}, and A225546 provides a self-inverse bijection between the two sets. - _Peter Munn_, Jul 19 2020

%H T. D. Noe, <a href="/A028983/b028983.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ n. - _Charles R Greathouse IV_, Jan 11 2013

%F a(n) = n + (1 + sqrt(2)/2)*sqrt(n) + O(1). - _Charles R Greathouse IV_, Sep 01 2015

%F A007913(a(n)) > 2. - _Peter Munn_, May 05 2020

%t Select[Range[82],EvenQ[DivisorSigma[1,#]]&] (* _Jayanta Basu_, Jun 05 2013 *)

%o (PARI) is(n)=!issquare(n)&&!issquare(n/2) \\ _Charles R Greathouse IV_, Jan 11 2013

%Y Complement of A028982.

%Y Cf. A000203, A000593, A001227, A007913, A178910, A152678.

%Y Subsequences: A083207, A091067, A145204\{0}, A225838, A225858.

%Y Cf. A334748 (a permutation).

%Y Related to A008586 via A225546.

%K nonn,easy

%O 1,1

%A _Patrick De Geest_

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)