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Search: id:A073815
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| A073815 |
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Least number x such that GCD[Phi[x],Sigma[x]]=n. |
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+0
6
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| 1, 3, 18, 12, 200, 14, 3364, 15, 722, 328, 9801, 42, 25281, 116, 1800, 165, 36992, 810, 4414201, 88, 196, 29161, 541696, 35, 2928200, 1413, 103968, 172, 98942809, 488, 1547536, 336, 19602, 17536, 814088, 370, 49042009, 55297, 1521, 319, 3150464641
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OFFSET
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1,2
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COMMENT
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Values are frequently identical to terms of A077102. Since GCD[a,b] and GCD[a+b,a-b] may differ, so may the smallest solutions. A077102(m) and a(m) differ e.g. at m=1,2,4,8,16,28,32,40 etc..
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FORMULA
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a(n)=Min{x; A055008(x)=n}. a(n)=Min{x; GCD[A000203(x), A000010(x)]=n}
Also a(n)=Min{x: A023897(x)= n}, smallest balanced number (A020492) for which the quotient equals n.
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EXAMPLE
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n=19: a(n)=x=4424201,Phi[x]=3991900,Sigma[x]=4977509, GCD[3991900,4977509]=19.
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MATHEMATICA
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f[x_] := Apply[GCD, {DivisorSigma[1, x], EulerPhi[x]}] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10^13}];
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CROSSREFS
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Cf. A000203, A000010, A055008, A077099-A077102, A051612, A065387.
Cf. A023897, A020492.
Sequence in context: A007475 A098874 A077104 this_sequence A103715 A131860 A048080
Adjacent sequences: A073812 A073813 A073814 this_sequence A073816 A073817 A073818
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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), Nov 12 2002
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