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Search: id:A078538
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| A078538 |
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Smallest x such that sigma[n,x]/phi[x] is an integer larger than 6. |
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+0
5
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| 12, 22, 12, 249, 12, 22, 12, 19689, 12, 22, 12, 249, 12, 22, 12
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For n=16,48,64 and 80 the solutions are hard to find, exceed 10^6 or even 10^7.
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EXAMPLE
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These terms appear as 5th entries in A020492, A015759-A015774. x={1, 2, 3, 6} are solutions to Min{x : Mod[sigma[n, x], phi[x]]=0}. First nontrivial solutions are larger: for odd n, x=12 is solution; for even powers larger numbers arise like 22, 249, 9897, 19689, etc. Certain power-sums of divisors proved to be hard to find.
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MATHEMATICA
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f[k_, x_] := DivisorSigma[k, x]/EulerPhi[x] Table[fl=1; Do[s=f[k, n]; If[IntegerQ[s]&&Greater[n, 6], Print[{n, k}; fl=0], {n, 1, 100000}, {k, 1, 100}]
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CROSSREFS
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Cf. A000203, A001157, A001158, A000010, A015759-A015774, A020492.
Sequence in context: A114015 A065439 A031186 this_sequence A098955 A124885 A115745
Adjacent sequences: A078535 A078536 A078537 this_sequence A078539 A078540 A078541
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KEYWORD
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hard,more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 29 2002
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