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Search: id:A082057
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| A082057 |
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Least x=a[n] such that product of common prime-divisors [without multiplicity] of sigma[x] and phi[x] equals n; or 0 if n is not a square-free number or if no such x exists. Among indices n only square-free numbers arise because multiplicity of prime factors is ignored. |
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+0
1
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| 1, 3, 18, 0, 200, 14, 3364, 0, 0, 88, 9801, 0, 25281, 116, 1800, 0, 36992, 0, 4414201, 0, 196, 2881, 541696, 0, 0, 711, 0, 0, 98942809, 209, 1547536, 0, 19602, 6901, 814088, 0, 49042009, 8473, 1521, 0, 3150464641, 377, 245178368, 0, 0, 6439, 9265217536, 0, 0
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n)=Min{x; A082055[x]=n}; 0 if n is not square-free.
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EXAMPLE
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n = 85: a(n) = 924800 = 128.5.5.17.17; sigma[924800] = 2426835 = 3.5.17.31.307; phi[924800] = 348160 = 4096.5.17; common prime factor 5.17 = n.
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]]
lf[x_] := Length[FactorInteger[x]]
ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]
t=Table[0, {100}]; Do[s=Apply[Times, Intersection
[ba[EulerPhi[n]], ba[DivisorSigma[1, n]]]];
If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}]; t
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CROSSREFS
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Cf. A000203, A000010, A082054-A082056.
Cf. A073815.
Sequence in context: A162713 A161473 A082056 this_sequence A161687 A120647 A131635
Adjacent sequences: A082054 A082055 A082056 this_sequence A082058 A082059 A082060
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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), Apr 03 2003
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EXTENSIONS
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Corrected and extended by David Wasserman (wasserma(AT)spawar.navy.mil), Aug 27 2004
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