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A127725
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Numbers n that are 2-imperfect.
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6
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OFFSET
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1,1
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COMMENTS
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This sequence also contains n = 3074457344902430720 = 2^31*5*17*257*65537, which has the product of four Fermat primes (A019434). For this n, 3*n is a 3-imperfect number (A127726). [T. D. Noe, Apr 03 2009]
a(9) > 2*10^11. - Donovan Johnson, Feb 07 2013
62549517598720 is also a term (see the "43 terms > 2*10^11" link by Donovan Johnson in A127724). - Michel Marcus, Nov 05 2017
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LINKS
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Table of n, a(n) for n=1..9.
Laszlo Toth, The alternating sum-of-divisors function, 9th Joint Conf. on Math. and Comp. Sci., February 9-12, 2012, Siofok, Hungary.
Laszlo Toth, A survey of the alternating sum-of-divisors function, arXiv:1111.4842 [math.NT], 2011-2014.
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EXAMPLE
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40=2^3*5. (8-4+2-1)(5-1) = 20, 2*20 = 40, so 40 is in the sequence. - Jud McCranie, Aug 17 2019
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MATHEMATICA
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okQ[n_] := 2 Sum[d*(-1)^PrimeOmega[n/d], {d, Divisors[n]}] == n;
For[k = 2, k <= 10^9, k = k+2, If[okQ[k], Print[k]]] (* Jean-François Alcover, Jan 27 2019 *)
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PROG
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(PARI) isok(n) = 2*sumdiv(n, d, d*(-1)^bigomega(n/d)) == n; \\ Michel Marcus, Oct 28 2017
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CROSSREFS
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Cf. A127726 (3-imperfect numbers), A127724 (k-imperfect numbers).
Sequence in context: A003683 A188572 A098519 * A280174 A185619 A048014
Adjacent sequences: A127722 A127723 A127724 * A127726 A127727 A127728
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KEYWORD
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nonn,more,hard
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AUTHOR
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T. D. Noe, Jan 25 2007
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EXTENSIONS
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a(9) by Jud McCranie, Aug 17 2019
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STATUS
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approved
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