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A038843
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Super unitary perfect numbers: usigma(usigma(n)) = 2*n, where if n = Product p(i)^r(i) then usigma(n) = Product (p(i)^r(i)+1).
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2
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2, 9, 165, 238, 1640, 4320, 10250, 10824, 13500, 23760, 58500, 66912, 425880, 520128, 873180, 931392, 1899744, 2129400, 2253888, 3276000, 4580064, 4668300, 13722800, 15459840, 40360320, 201801600, 439021440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| May be called (2,2)-unitary perfect numbers, analogous to (k,l)-perfect numbers.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
| usigma[n_] := Times @@ (Apply[ Power, FactorInteger[n], {1}] + 1); n = 1; A038843 = {}; While[n < 10^7, If[ usigma[ usigma[n] ] == 2n, Print[n]; AppendTo[ A038843, n] ]; n++]; A038843 (* From Jean-François Alcover, Dec 07 2011 *)
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PROG
| (PARI) {usigma(n, s=1, fac, i)= fac=factor(n); for(i=1, matsize(fac)[1], s=s*(1+fac[i, 1]^fac[i, 2]) ); return(s); } for(n=1, 10^7, if(usigma(usigma(n))==2*n, print1(n, ", ")))
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CROSSREFS
| Cf. A038843, A034448.
Sequence in context: A133468 A182948 A081459 * A053294 A199695 A078524
Adjacent sequences: A038840 A038841 A038842 * A038844 A038845 A038846
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KEYWORD
| nonn,nice
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AUTHOR
| Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)
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EXTENSIONS
| Corrected by Jason Earls (zevi_35711(AT)yahoo.com), Aug 25 2001. More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Oct 28 2001
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