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Search: id:A099632
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| A099632 |
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Numbers n for which (sigma[n-d]+sigma[n+d])/2 = sigma[n], where d=1; name=1-sigma-balanced numbers. |
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+0
2
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| 45, 694, 3768374, 6303735, 15913725, 20291271, 42824146, 47788894, 54424095
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OFFSET
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1,1
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COMMENT
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These terms, the 1-sigma-balanced numbers, seems to be significantly rarer than those with d=2,4,6,8,10.. It seems also that the 6-sigma-balanced numbers are very common.
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FORMULA
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Solutions to sigma[x-d]+sigma[x+d]=2*sigma[x] where d=1. n=20291271, a=sigma[n-1]=37374480, b=sigma[n+1]=38104560 sigma[n]=37739520=(a+b)/2,
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MATHEMATICA
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d=1; Do[s=(DivisorSigma[1, n+d]+DivisorSigma[1, n-d])/ 2-DivisorSigma[1, n]; If[Equal[s, 0], Print[n]], {n, 1, 100000000}]
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CROSSREFS
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Cf. A000203, A099631.
Sequence in context: A090024 A110691 A105251 this_sequence A024379 A134290 A078761
Adjacent sequences: A099629 A099630 A099631 this_sequence A099633 A099634 A099635
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 26 2004
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