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 A028983 Numbers n such that the sum of the divisors of n is even. 33
 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 82 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The even terms of this sequence are the even terms appearing in A178910. [Edited by M. F. Hasler, Oct 02 2014] A071324(a(n)) is even. - Reinhard Zumkeller, Jul 03 2008 Sigma(a(n)) = A000203(a(n)) = A152678(n). - Jaroslav Krizek, Oct 06 2009 A083207 is a subsequence. - Reinhard Zumkeller, Jul 19 2010 Numbers n such that the number of odd divisors of n (A001227) is even. - Omar E. Pol, Apr 04 2016 Numbers n such that the sum of odd divisors of n (A000593) is even. - Omar E. Pol, Jul 05 2016 Numbers with a squarefree part greater than 2. - Peter Munn, Apr 26 2020 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 FORMULA a(n) ~ n. - Charles R Greathouse IV, Jan 11 2013 a(n) = n + (1 + sqrt(2)/2)*sqrt(n) + O(1). - Charles R Greathouse IV, Sep 01 2015 A007913(a(n)) > 2. - Peter Munn, May 05 2020 MATHEMATICA Select[Range[82], EvenQ[DivisorSigma[1, #]]&] (* Jayanta Basu, Jun 05 2013 *) PROG (PARI) is(n)=!issquare(n)&&!issquare(n/2) \\ Charles R Greathouse IV, Jan 11 2013 CROSSREFS Complement of A028982. Cf. A000203, A000593, A001227, A007913, A178910, A152678. Subsequences: A083207, A091067, A145204\{0}, A225838, A225858. Cf. A334748 (a permutation). Related to A008586 via A225546. Sequence in context: A055597 A053048 A154663 * A232682 A335657 A038550 Adjacent sequences:  A028980 A028981 A028982 * A028984 A028985 A028986 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)