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A078540
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Least non-balanced x (i.e. not in A020492) such that sigma(p(n),x)/phi(x) is an integer, where p(n)=n-th prime.
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2
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22, 38, 46, 295, 235, 749, 3687, 6128, 1415, 4254, 10451, 8351, 334, 4511, 3398, 1286, 148870, 11051, 35519, 10239, 14072, 76088, 5991, 718, 11654, 30761, 7431, 20993, 700654, 22169, 5095, 4198, 27415, 26744, 14318, 48368, 180878, 16991
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..38.
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FORMULA
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a(n)=Min{x; Mod[A000203[x], A000005[x]]=0 but Mod[sigma[A000040[n], x], phi[x]]is not 0}
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EXAMPLE
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n=6: p(6)=13, cases of sig[13,x]/phi[x] is an integer are listed in A015771: 1,2,3,6,12,..etc; the first term which is non-balanced, i.e. not in A020492 is a(6)=749=A020492(31); a(29)=700854 and a(45)=510759 are remarkably large.
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MATHEMATICA
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Table[fl=1; Do[s1=DivisorSigma[1, n]/EulerPhi[n]; sk=DivisorSigma[Prime[k], n]/EulerPhi[n]; If[ !IntegerQ[s1]&&IntegerQ[sk]&&Equal[fl, 1], Print[{n, Prime[k]}]; fl=0], {n, 1, 1000000}], {k, 1, 100}]
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CROSSREFS
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Cf. A020492, A015759-A015774, A078538, A078539 A000010, A000005, A000040.
Sequence in context: A084141 A082261 A063252 * A057836 A078612 A039373
Adjacent sequences: A078537 A078538 A078539 * A078541 A078542 A078543
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 02 2002
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STATUS
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approved
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