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%I #69 Aug 24 2022 09:47:21
%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
%C Also numbers whose reversed prime indices have alternating product > 1, where we define the alternating product of a sequence (y_1,...,y_k) to be Product_i y_i^((-1)^(i-1)). Also Heinz numbers of the partitions counted by A347448. - _Gus Wiseman_, Oct 29 2021
%C Numbers whose number of middle divisors is not odd (cf. A067742). - _Omar E. Pol_, Aug 02 2022
%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 The complement is A028982 = A000290 U A001105.
%Y Cf. A000203, A000593, A001227, A007913, A178910, A152678, A067742.
%Y Subsequences: A083207, A091067, A145204\{0}, A225838, A225858.
%Y Cf. A334748 (a permutation).
%Y Related to A008586 via A225546.
%Y Ranks the partitions counted by A347448, complement A119620.
%Y Cf. A030059, A335433, A335448, A339890, A344607, A347438, A347443, A347445, A347446, A347452, A347453, A347465.
%K nonn,easy
%O 1,1
%A _Patrick De Geest_
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