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Search: id:A015759
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| A015759 |
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Numbers n such that phi(n) | sigma_2(n). |
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+0
9
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| 1, 2, 3, 6, 22, 33, 66, 750, 27798250, 41697375, 76745867, 83394750, 153491734
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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sigma_2(n) is the sum of the squares of the divisors of n (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 E. (labos(AT)ana.sote.hu), May 25 2004
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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 [eg 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)
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CROSSREFS
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Cf. A093643.
Cf. A015765, A015768, A094470.
Sequence in context: A015768 A094470 A015764 this_sequence A000616 A018300 A027163
Adjacent sequences: A015756 A015757 A015758 this_sequence A015760 A015761 A015762
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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a(9) - a(13) from Labos E. (labos(AT)ana.sote.hu), May 20 2004
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