cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A064375 Numbers n such that sigma_2(n) > phi(n)^3.

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%I A064375 #7 Nov 19 2015 17:16:47
%S A064375 2,3,4,6,8,10,12,14,18,20,24,30,36,42,60
%N A064375 Numbers n such that sigma_2(n) > phi(n)^3.
%C A064375 This sequence is finite, since by Grönwall's theorem sigma_2(n) <= sigma(n)^2 << (n log log n)^2 but phi(n)^3 >> (n/log log n)^3. - _Charles R Greathouse IV_, Nov 18 2015
%F A064375 Solutions to A001157(n) > A000010(x)^3.
%e A064375 d-square sums:{5, 10, 21, 50, 85, 130, 210, 250, 455, 546, 850, 1300, 1911, 2500, 5460} phi-cubes:{1, 8, 8, 8, 64, 64, 64, 216, 216, 512, 512, 512, 1728, 1728, 4096} differences:{4, 2, 13, 42, 21, 66, 146, 34, 239, 34, 338, 788, 183, 772, 1364} Sequence is believed to be full.
%t A064375 Select[Range[100],DivisorSigma[2,#]>EulerPhi[#]^3&] (* _Harvey P. Dale_, Feb 19 2013 *)
%o A064375 (PARI) is(n)=my(f=factor(n)); sigma(f,2)>eulerphi(f)^3 \\ _Charles R Greathouse IV_, Nov 18 2015
%Y A064375 Cf. A001157, A000010, A055234.
%K A064375 nonn,fini
%O A064375 1,1
%A A064375 _Labos Elemer_, Sep 27 2001