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A038843
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Unitary superperfect numbers: numbers n such that usigma(usigma(n)) = 2*n, where usigma(n) is the sum of unitary divisors of n (A034448).
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7
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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, 3809332800, 15359485680, 794436968640, 1407035080704
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OFFSET
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1,1
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COMMENTS
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May be called (2,2)-unitary perfect numbers, analogous to (k,l)-perfect numbers.
Sitaramaiah and Subbarao found the first 22 terms. Also in the sequence is 12189313382400. - Amiram Eldar, Feb 27 2019
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LINKS
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Tomohiro Yamada, Unitary super perfect numbers, Mathematica Pannonica, Volume 19, No. 1, 2008, pp. 37-47; Preprint, arXiv:0802.4377 [math.NT], 2008. Proves that 9 and 165 are the only odd terms of this sequence.
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MATHEMATICA
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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 (* Jean-François Alcover, Dec 07 2011 *)
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PROG
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(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
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Cf. A064012 (usigma(usigma(n)) = 3n).
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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