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A122483
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Numbers m such that A049060(m)*sigma(m) = k*uphi(m)*m for some integer k.
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1
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6, 140, 312, 1560, 14384, 18018, 40992, 2337400, 7012200, 11027016, 231402600, 534775296, 9866296440, 11453072202
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OFFSET
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1,1
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COMMENTS
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If both 2^n-3 and 2^n-1 are prime then numbers of the form 2^(n-1)*(M_n-2)*M_n appear in the sequence, where M_n means Mersenne prime.
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LINKS
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Table of n, a(n) for n=1..14.
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EXAMPLE
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2^8*7*19*37*73*509, 2^8*5*7*19*37*509, 2^8*5^2*7*19*29*31*37*509, 2^9*3*11*31*1021, 2^9*3*7*11^2*19*31*131*1021, 2^11*3^6*5*7*13*23*137*467*1093*4093, 2^13*3*11*43*127*16381, 2^13*3*7*11^2*19*43*127*131*16381 are terms, but there may be many other terms between 3*10^7 and them.
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MATHEMATICA
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f[p_, e_] := (p^(e+1)-2*p+1) * (p^(e+1)-1)/((p-1)^2 * (p^e - 1)); q[n_] := IntegerQ[(Times @@ f @@@ FactorInteger[n])/n]; Select[Range[2, 10^5], q] (* Amiram Eldar, Sep 19 2022 *)
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CROSSREFS
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Cf. A123124, A000203 (sigma), A047994 (uphi), A049060.
Sequence in context: A007340 A335318 A342358 * A335369 A335388 A123729
Adjacent sequences: A122480 A122481 A122482 * A122484 A122485 A122486
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KEYWORD
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nonn,more
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AUTHOR
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Yasutoshi Kohmoto, Sep 30 2006
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EXTENSIONS
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More terms from R. J. Mathar, Oct 01 2006
a(12)-a(14) from Amiram Eldar, Sep 19 2022
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STATUS
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approved
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