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A347222
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Numbers k for which sigma(k)/k = 12/5.
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0
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30, 140, 2480, 6200, 40640, 167751680, 42949345280, 687193456640, 11529215040699760640, 13292279957849158723273463079769210880, 957809713041180536473966890421518190654986607740846080, 65820182292848241686198767302293614551117361591934715588918640640
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OFFSET
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1,1
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COMMENTS
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This sequence will contain terms of the form 5*P, where P is a perfect number (A000396) not divisible by 5. Proof: sigma(5*P)/(5*P) = sigma(5)*sigma(P)/(5*P) = 6*(2*P)/(5*P) = 12/5. QED
Terms ending in "30", "40", or "80" have this form. Example: a(n) = 5*A000396(n) for n = 1, 2, 3 and a(n) = 5*A000396(n-1) for n = 5..12.
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LINKS
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EXAMPLE
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6200 is a term, since sigma(6200)/6200 = 14880/6200 = 12/5.
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MATHEMATICA
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Select[Range[5*10^8], DivisorSigma[1, #]/# == 12/5 &]
Do[If[DivisorSigma[1, k]/k == 12/5, Print[k]], {k, 5*10^8}]
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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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