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 A088828 Nonsquare positive odd numbers. 11
 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 123, 125, 127, 129, 131, 133, 135, 137, 139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Odd numbers with even abundance: primes and some composites too. Odd numbers with odd abundance are in A016754. Even numbers with odd abundance are in A088827. Even numbers with even abundance are in A088829. Or, odd numbers without the squares. - Gerald Hillier, Apr 12 2009 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = 2*n + s - ((s+1) mod 2) where s = round(sqrt(2*n-1)). - Gerald Hillier, Apr 15 2009 A005408 SETMINUS A016754. - R. J. Mathar, Jun 16 2018 a(n) = 2*(n+h) + 1 where h = floor((1/4)*(sqrt(8*n) - 1)) is the largest value such that A014105(h) < n. - John Tyler Rascoe, Jul 05 2022 EXAMPLE n = p prime, abundance = 1 - p = even and negative; n = 21, sigma = 1 + 3 + 7 + 21 = 32, abundance = 32 - 42 = -20. MATHEMATICA Do[s=DivisorSigma[1, n]-2*n; If[ !OddQ[s]&&OddQ[n], Print[{n, s}]], {n, 1, 1000}] Select[Range[1, 500, 2], EvenQ[DivisorSigma[1, #] - 2 #] &] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *) PROG (Magma) [ n: n in [1..140 by 2] | IsEven(SumOfDivisors(n)-2*n) ]; // Klaus Brockhaus, Apr 15 2009 (PARI) isok(n) = (n>0) && (n % 2) && ! issquare(n); \\ Michel Marcus, Aug 28 2013 CROSSREFS Cf. A005408, A014105, A016754, A088827, A088829, A157502. Sequence in context: A352830 A320056 A175679 * A348741 A348748 A182318 Adjacent sequences:  A088825 A088826 A088827 * A088829 A088830 A088831 KEYWORD nonn,easy AUTHOR Labos Elemer, Oct 28 2003 EXTENSIONS Entry revised by N. J. A. Sloane, Jan 31 2014 at the suggestion of Omar E. Pol STATUS approved

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Last modified September 26 18:11 EDT 2022. Contains 357002 sequences. (Running on oeis4.)