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A078539
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Least non-balanced x [i.e. not in A020492] such that sigma[2n-1,x]/phi[x] is an integer.
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10
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38, 46, 295, 38, 235, 749, 38, 3687, 6128, 38, 1415, 46, 38, 4254, 10451, 38, 46, 8351, 38, 334, 4511, 38, 3398, 295, 38, 1286, 46, 38, 148870, 11051, 38, 46, 35519, 38, 10239, 14072, 38, 235, 76088, 38, 5991, 46, 38, 718, 295, 38, 46, 11654, 38, 30761
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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FORMULA
| a(n)=Min{x; Mod[sigma[1, x], phi[x]]=0 but Mod[sigma[2n-1, x], phi[x]]is not 0}
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EXAMPLE
| n=7: 2n-1=13, cases of sig[13,x]/phi[x] is an integer listed in A015771: 1,2,3,6,12,..etc; the first term which is non-balanced, i.e. not in A020492 is a(7)=749=A020492(31); Increasing n, trend of a(n) is roughly the same. If 2n-1=3s, i.e. is divisible with 3, then a[3s]=38. Similar relationships hold for 2n-1=5s,7s,11s, etc..
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MATHEMATICA
| Table[fl=1; Do[s1=DivisorSigma[1, n]/EulerPhi[n]; sk=DivisorSigma[2*k-1, n]/EulerPhi[n]; If[ !IntegerQ[s1]&&IntegerQ[sk]&&Equal[fl, 1], Print[{n, 2*k-1}]; fl=0], {n, 1, 1000000}], {k, 2, 100}]
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CROSSREFS
| Cf. A020492, A015759-A015774, A078538, A000010, A000005.
Sequence in context: A078550 A133123 A177222 * A125970 A026047 A039352
Adjacent sequences: A078536 A078537 A078538 * A078540 A078541 A078542
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Dec 02 2002
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