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A099632
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1-sigma-balanced numbers: numbers n such that (sigma(n-d)+sigma(n+d))/2 = sigma(n) for d=1.
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7
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45, 694, 3768374, 6303735, 15913725, 20291271, 42824146, 47788894, 54424095, 141120134, 163380694, 219105494, 305034794, 404686557, 790565966, 893558445, 928608435, 1198745925, 1251276254, 1409720194, 1412229015, 1696122945
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OFFSET
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1,1
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COMMENTS
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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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LINKS
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FORMULA
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Solutions to sigma(x-d)+sigma(x+d)=2*sigma(x) where d=1.
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EXAMPLE
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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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PROG
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(PARI) is(n) = n>1 && (sigma(n-1)+sigma(n+1))/2==sigma(n) \\ Felix Fröhlich, Sep 03 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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