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A067808 Numbers k such that sigma(k)^2 > 3*sigma(k^2). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For every m>1 sigma(m)^2 > sigma(m^2).

From Robert Israel, Jun 20 2018: (Start)

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)

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

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:

select(filter, [$1..10^4]); # Robert Israel, Jun 20 2018

MATHEMATICA

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];

Select[Range[10^4], filterQ] (* Jean-Fran├žois Alcover, Apr 29 2019, after Robert Israel *)

PROG

(PARI) isok(k) = sigma(k)^2 > 3*sigma(k^2); \\ Michel Marcus, Apr 29 2019

CROSSREFS

Cf. A002110, A065764.

Sequence in context: A257416 A137493 A179669 * A302127 A291804 A131663

Adjacent sequences:  A067805 A067806 A067807 * A067809 A067810 A067811

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 07 2002

STATUS

approved

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Last modified February 25 05:01 EST 2020. Contains 332217 sequences. (Running on oeis4.)