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Search: id:A088828
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| A088828 |
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Odd numbers with even abundance: primes and some composites too. |
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+0
4
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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. [From Gerald Hillier (adr.rabbicat(AT)gmail.com), Apr 12 2009]
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FORMULA
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Set S=ROUND(SQRT(2*n-1),0) then a(n)=2*n+S-((S+1) MOD 2) [From Gerald Hillier (adr.rabbicat(AT)gmail.com), Apr 15 2009]
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EXAMPLE
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n=p prime, abundance=1-p=even and negative;
n=21, sigma=1+3+7+21=32,abundance=32-42=-20;
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MATHEMATICA
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Do[s=DivisorSigma[1, n]-2*n; If[ !OddQ[s]&&OddQ[n], Print[{n, s}]], {n, 1, 1000}]
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PROGRAM
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(MAGMA) [ n: n in [1..140 by 2] | IsEven(SumOfDivisors(n)-2*n) ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 15 2009]
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CROSSREFS
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Cf. A016754, A088827-A088829.
Sequence in context: A161554 A070087 A100933 this_sequence A056911 A152955 A155113
Adjacent sequences: A088825 A088826 A088827 this_sequence A088829 A088830 A088831
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 28 2003
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