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Search: id:A030165
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| A030165 |
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Numbers n such that uphi(sigma(n))=2n, where the unitary phi function (A047994) is defined by: if x=p1^r1*p2^r2*p3^r3*... then uphi(x)=(p1^r1-1)(p2^r2-1)(p3^r3-1)... |
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1
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| 36, 252, 288, 756, 1116, 1512, 2016, 4572, 6048, 8928, 24192, 36576, 62208, 115200, 136080, 294876, 806400, 2359008, 2419200, 3571200, 4147200, 4718556, 6193152, 10782720, 14630400, 18874332, 20575296, 29030400, 30108672, 37748448
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OFFSET
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1,1
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COMMENT
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Theorem: If m is in the sequence, sigma(m) is an odd number, 2^n-1 is a prime greater than 3 (a Mersenne prime) and gcd(m, 2^n-1)=1 then m*(2^n-1) is in the sequence (the proof is easy). One of the results of this theorem is: If p=2^n-1 is a prime greater than 3 then 36*p, 288*p,115200*p and 4147200*p are in the sequence. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Jul 08 2006
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MATHEMATICA
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uphi[n_] := (A = FactorInteger[n]; l = Length[A]; Product[A[[k]][[1]] ^A[[k]][[2]] - 1, {k, l}]); Do[If[uphi[DivisorSigma[1, n]] == 2n, Print[n]], {n, 70000000}] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Jul 08 2006
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CROSSREFS
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Sequence in context: A159921 A129149 A074363 this_sequence A017342 A115332 A133072
Adjacent sequences: A030162 A030163 A030164 this_sequence A030166 A030167 A030168
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KEYWORD
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nonn
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AUTHOR
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Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)
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EXTENSIONS
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Corrected and extended by Farideh Firoozbakht (mymontain(AT)yahoo.com), Jul 08 2006
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