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.

A070004 Numbers of the form 5*2^n or 5*3*2^n; a(n) = 5*A029744(n).

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%I A070004 #28 Jan 02 2021 05:00:32
%S A070004 5,10,15,20,30,40,60,80,120,160,240,320,480,640,960,1280,1920,2560,
%T A070004 3840,5120,7680,10240,15360,20480,30720,40960,61440,81920,122880,
%U A070004 163840,245760,327680,491520,655360,983040,1310720,1966080,2621440
%N A070004 Numbers of the form 5*2^n or 5*3*2^n; a(n) = 5*A029744(n).
%C A070004 Old name was: Numbers n such that phi(P(n)) - P(phi(n)) = 2, where P(x)=largest prime factor of x, or A000010(A006530(n))-A006530(A000010(n))=2.
%C A070004 Solutions to phi(P(x))-P(phi(x))=c, presence or absence of special prime factors in x are usually derivable.
%H A070004 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A070004 a(n) = 5*A029744(n); numbers of the forms 5*2^n and 15*2^n.
%F A070004 G.f.: 5*x*(x+1)^2/(1-2*x^2). - _Ralf Stephan_, Jul 15 2013
%F A070004 Sum_{n>=1} 1/a(n) = 8/15. - _Amiram Eldar_, Jan 02 2021
%t A070004 pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2]; Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[Equal[s, 2], Print[n]], {n, 3, 1000000}]
%t A070004 Union[Flatten[Table[2^n {5,15},{n,0,20}]]] (* or *) Join[ {5}, LinearRecurrence[ {0,2},{10,15},40]] (* _Harvey P. Dale_, Dec 23 2014 *)
%o A070004 (PARI) gpf(n)=if(n>1,my(f=factor(n)[,1]);f[#f],1)
%o A070004 is(n)=eulerphi(gpf(n))-gpf(eulerphi(n))==2 \\ _Charles R Greathouse IV_, Feb 19 2013
%Y A070004 Cf. A000010, A006530, A068211, A070777, A070812, A070002, A070003, A007283, A070813-A070816.
%K A070004 nonn,easy
%O A070004 1,1
%A A070004 _Labos Elemer_, May 07 2002
%E A070004 Simpler name by _Joerg Arndt_, Jul 16 2013