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A081380
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Numbers k such that the sets of prime factors (ignoring multiplicity) of A000203(k) = sigma(k) and of A001157(k) = sigma_2(k) are identical.
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2
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1, 180, 1444, 12996, 23805, 36100, 52020, 60228, 64980, 68832, 95220, 301140, 324900, 344160, 481824, 1505700, 1718721, 1720800, 2275758, 2409120, 3755844, 6874884, 6879645, 7965153, 8593605, 11378790, 12045600, 15930306, 17405892
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OFFSET
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1,2
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REFERENCES
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Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 180, p. 56, Ellipses, Paris, 2008.
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LINKS
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EXAMPLE
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n = 1444 = 2^2*19^2, sigma(1444) = 2667 = 3*7*127, sigma_2(1444) = 2744343 = 3^2*7^4*127, common factor set = {3,7,127}.
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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]}]; Do[s=ba[DivisorSigma[1, n]]; s5=ba[DivisorSigma[2, n]]; If[Equal[s, s5], Print[n]], {n, 1, 1000000}]
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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