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A088828 Nonsquare positive odd numbers. 7
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

Table of n, a(n) for n=1..64.

FORMULA

Let s = round(sqrt(2*n-1)); then a(n) = 2*n + s - ((s+1) mod 2). - Gerald Hillier, Apr 15 2009

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. A016754, A088827, A088828, A088829, A157502.

Sequence in context: A070087 A100933 A175679 * A182318 A247424 A056911

Adjacent sequences:  A088825 A088826 A088827 * A088829 A088830 A088831

KEYWORD

nonn

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 February 20 02:07 EST 2018. Contains 299357 sequences. (Running on oeis4.)