

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
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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 selfinverse 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

Patrick De Geest


STATUS

approved



