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A028982 Squares and twice squares. 79
1, 2, 4, 8, 9, 16, 18, 25, 32, 36, 49, 50, 64, 72, 81, 98, 100, 121, 128, 144, 162, 169, 196, 200, 225, 242, 256, 288, 289, 324, 338, 361, 392, 400, 441, 450, 484, 512, 529, 576, 578, 625, 648, 676, 722, 729, 784, 800, 841, 882, 900, 961, 968, 1024 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that sum of divisors of n (A000203) is odd.

Also the numbers with an odd number of run sums (trapezoidal arrangements, number of ways of being written as the difference of two triangular numbers). - Ron Knott, Jan 27 2003

Pell(n)*Sum_{k|n} 1/Pell(k) is odd, where Pell(n) is A000129(n). - Paul Barry, Oct 12 2005

Number of odd divisors of n (A001227) is odd. - Vladeta Jovovic, Aug 28 2007

A071324(a(n)) is odd. - Reinhard Zumkeller, Jul 03 2008

Sigma(a(n)) = A000203(a(n)) = A152677(n). - Jaroslav Krizek, Oct 06 2009

Numbers n such that sum of odd divisors of n (A000593) is odd. - Omar E. Pol, Jul 05 2016

A187793(a(n)) is odd. - Timothy L. Tiffin, Jul 18 2016

If k is odd (k = 2m+1 for m >= 0), then 2^k = 2^(2m+1) = 2*(2^m)^2.  If k is even (k = 2m for m >= 0), then 2^k = 2^(2m) = (2^m)^2.  So, the powers of 2 sequence (A000079) is a subsequence of this one. - Timothy L. Tiffin, Jul 18 2016

Numbers n such that A175317(n) = Sum_{d|n} pod(d) is odd, where pod(m) = the product of divisors of m (A007955). - Jaroslav Krizek, Dec 28 2016

Positions of zeros in A292377 and A292383, positions of ones in A286357 and A292583. (See A292583 for why.) - Antti Karttunen, Sep 25 2017

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, Journal of Integer Sequences, Vol. 16 (2013), #13.1.8.

P. De Geest, World!Of Numbers

John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type, Acta Cryst. (2009). A65, 156-163.

Eric Weisstein's World of Mathematics, Abundance

FORMULA

a(n) is asymptotic to c*n^2 with c = 2/(1+sqrt(2))^2 = 0.3431457.... - Benoit Cloitre, Sep 17 2002

In particular, a(n) = cn^2 + O(n). - Charles R Greathouse IV, Jan 11 2013

a(A003152(n))= n^2;  a(A003151(n))=2*n^2. - Enrique Pérez Herrero, Oct 09 2013

MATHEMATICA

Take[ Sort[ Flatten[ Table[{n^2, 2n^2}, {n, 35}] ]], 57] (* Robert G. Wilson v, Aug 27 2004 *)

PROG

(PARI) list(lim)=vecsort(concat(vector(sqrtint(lim\1), i, i^2), vector(sqrtint(lim\2), i, 2*i^2))) \\ Charles R Greathouse IV, Jun 16 2011

(Haskell)

import Data.List.Ordered (union)

a028982 n = a028982_list !! (n-1)

a028982_list = tail $ union a000290_list a001105_list

-- Reinhard Zumkeller, Jun 27 2015

CROSSREFS

Complement of A028983.

Characteristic function is A053866, A093709.

Odd terms in A178910.

Union of A000290 and A001105.

Cf. A000203, A000593, supersequence of A000079, A187793.

Sequence in context: A155562 A048715 A242662 * A175338 A071601 A114400

Adjacent sequences:  A028979 A028980 A028981 * A028983 A028984 A028985

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified October 18 00:56 EDT 2017. Contains 293484 sequences.