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A072808
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Smallest m such that Mod[sigma[m],phi[m]]=n.
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0
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4, 5, 8, 24, 0, 22, 16, 21, 450, 40, 25, 48, 50, 136, 32, 110, 100, 90, 144, 88, 0, 656, 121, 102, 0, 80, 169, 96, 0, 68, 64, 55, 676, 464, 289, 65, 0, 117, 162, 91, 0, 116, 225, 85, 0, 272, 529, 95, 0, 148, 288, 133, 0, 164, 0, 115, 0, 160, 841, 147, 0, 333, 128, 247
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n)=Min{x; Mod[A000203(x), A000010(x)]=n} or 0 if apparently no solutions.
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EXAMPLE
| n=4: a(4)=24 since sigma[24]=60, phi[24]=8 and Mod[60, 8]=4. Conjectured that no solutions for {5, 21, 25, 29, 37, 41, 45, 49, 53, 55, 57, 61, 67, 71, 77, 79, 85, 89, 99} No solutions found below 10000000000 for n values where 0 is written. For odd remainders a(n) is square or 2.square.
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MATHEMATICA
| f[x_] := Mod[DivisorSigma[1, x], EulerPhi[x]] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10000000000}];
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CROSSREFS
| Cf. A000203, A000010.
Sequence in context: A050892 A145265 A171938 * A104884 A113726 A140315
Adjacent sequences: A072805 A072806 A072807 * A072809 A072810 A072811
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 12 2002
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