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A015759
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Numbers k such that phi(k) | sigma_2(k).
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17
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1, 2, 3, 6, 22, 33, 66, 750, 27798250, 41697375, 76745867, 83394750, 153491734, 207656250, 230237601, 460475202, 917342250, 969062500, 2907187500, 4528006153, 5952812500, 9056012306, 13584018459, 17858437500, 27168036918, 31979062500, 57559400250
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OFFSET
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1,2
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COMMENTS
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sigma_2(k) is the sum of the squares of the divisors of k (A001157).
All of these terms are solutions to relations for all j as follows: {sigma(j,x)/phi(x) is integer for exponents j=4k+2}. Proof is possible by individual managements in the knowledge of divisors of x and phi(x). Compare with A015765, A015768, etc. - Labos Elemer, May 25 2004
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LINKS
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MATHEMATICA
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Do[ If[ IntegerQ[ DivisorSigma[2, n]/EulerPhi[n]], Print[n]], {n, 1, 10^7}]
Empirical test for very high power sums of divisors [e.g., d^2802]. Table[{4*j+2, Union[Table[IntegerQ[DivisorSigma[4*j+2, Part[t, k]]/EulerPhi[Part[t, k]]], {k, 1, 13}]]}, {j, 0, 700}] Output = {True} for all 4j+2. Here t=A015759. (* Labos Elemer, May 20 2004 *)
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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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