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Search: id:A082901
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| A082901 |
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a(n) = A082895(n)-A000203(n), that is difference of sigma[1,n] and the closest number divisible by n. |
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+0
4
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| 0, 1, -1, 1, -1, 0, -1, 1, -4, 2, -1, -4, -1, 4, 6, 1, -1, -3, -1, -2, 10, 8, -1, 12, -6, 10, -13, 0, -1, -12, -1, 1, -15, 14, -13, 17, -1, 16, -17, -10, -1, -12, -1, 4, 12, 20, -1, 20, -8, 7, -21, 6, -1, -12, -17, -8, -23, 26, -1, 12, -1, 28, 22, 1, -19, -12, -1, 10, -27, -4, -1, 21, -1, 34, 26, 12, -19, -12, -1, -26, -40, 38, -1, 28
(list; graph; listen)
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OFFSET
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1,9
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FORMULA
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a(n)=n*floor[(floor(n/2)+sigma[1, n])/n]-sigma[1, n]
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EXAMPLE
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n=2: sigma[2]=3, 2-divisible closest to 3 is 2(or 4), so a(2)=1.
n=28: sigma[1, 28]=56; so a 28-divisible number, closest to 28 is 28, so the difference is zero; zero-sites for this sequence are the (multiply) perfect numbers.
n=p=prime>2: sigma[p]=p+1, thus p-divisible and closest to p number is p, so difference is -1.
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MATHEMATICA
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Table[n*Floor[(Floor[n/2]+DivisorSigma[1, n])/n]- DivisorSigma[1, n], {n, 1, 100}]
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CROSSREFS
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Cf. A082893-A082900, A000203.
Sequence in context: A105698 A105699 A023526 this_sequence A136619 A132708 A016506
Adjacent sequences: A082898 A082899 A082900 this_sequence A082902 A082903 A082904
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KEYWORD
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sign
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Apr 22 2003
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