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A067808
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Numbers k such that sigma(k)^2 > 3*sigma(k^2).
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2
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720, 1080, 1440, 1680, 1800, 2016, 2160, 2520, 2880, 3024, 3240, 3360, 3600, 3780, 3960, 4032, 4200, 4320, 4680, 5040, 5280, 5400, 5544, 5760, 6048, 6120, 6300, 6480, 6720, 6840, 7056, 7200, 7560, 7920, 8064, 8400, 8640, 9000, 9072, 9240, 9360, 9504
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OFFSET
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1,1
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COMMENTS
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For every m>1 sigma(m)^2 > sigma(m^2).
Numbers with prime factorization Product_j p_j^(e_j) such that Product_j (p_j^(e_j+1)-1)^2/((p_j^(2*e_j+1)-1)*(p_j-1)) > 3.
If h is a member then so are all multiples of h.
The first member that is squarefree is 7420738134810 = A002110(12).
(End)
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LINKS
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MAPLE
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filter:= proc(n) local F;
F:= ifactors(n)[2];
mul((t[1]^(t[2]+1)-1)^2/(t[1]^(2*t[2]+1)-1)/(t[1]-1), t = F) > 3
end proc:
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MATHEMATICA
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filterQ[n_] := Module[{F = FactorInteger[n]}, If[n == 1, Return[False]]; Product[{p, e} = pe; (p^(e+1)-1)^2/((p^(2e+1)-1)(p-1)), {pe, F}] > 3];
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PROG
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(PARI) isok(k) = sigma(k)^2 > 3*sigma(k^2); \\ Michel Marcus, Apr 29 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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