%I #31 Jul 01 2021 03:39:43
%S 1,2,3,5,8,10,17,18,24,30,34,63,76,85,128,136,170,257,315,333,364,380,
%T 436,444,514,640,680,972,1285,1542,1820,1824,1836,1875,2142,2220,2907,
%U 3285,3488,3796,4369,4788,4860
%N Numbers k such that phi(k) (the totient function A000010) is a power of the number of divisors of k (A000005).
%C A019434 is a subsequence. - _David A. Corneth_, Jun 30 2017
%C Is the frequency of e such that A000005(a(n))^e = A000010(a(n)) finite? - _David A. Corneth_, Jul 01 2017
%H Charles R Greathouse IV, <a href="/A289276/b289276.txt">Table of n, a(n) for n = 1..5319</a> (first 526 terms from Antti Karttunen)
%t Join[{1},Select[Range[2,5000],IntegerQ[Log[DivisorSigma[0,#],EulerPhi[#]]]&]] (* _Harvey P. Dale_, Aug 06 2017 *)
%o (PARI) ispowerof(n, k)= if(k==1, return(n==1)); while(n>=k, if(n%k!=0, return(0)); n\=k); n==1
%o isa(n) = ispowerof(eulerphi(n),numdiv(n)) \\ Quick program, fast enough for early values.
%o (PARI) is(n) = if(n==1, return(1)); my(f = factor(n); phi = eulerphi(f), ndiv = numdiv(f), e = logint(phi, ndiv)); ndiv^e == phi \\ _David A. Corneth_, Jun 30 2017, changed per suggestion of _Charles R Greathouse IV_
%o (PARI) isA289276(n)= if(n==1, return(1)); my(phi = eulerphi(n), ndiv = numdiv(n), v = valuation(phi, ndiv)); ndiv^v == phi; \\ (A variant of above program). - _Antti Karttunen_, Jun 30 2017
%o (PARI) list(lim)=my(v=List([1])); forfactored(n=2,lim\1, my(phi = eulerphi(n), ndiv = numdiv(n)); if(ndiv^valuation(phi,ndiv) == phi, listput(v,n[1]))); Vec(v) \\ _Charles R Greathouse IV_, Jul 01 2017
%Y Cf. A000005, A000010, A019434, A020488, A032447, A036913, A051281, A068559, A068560, A114063, A286627.
%K nonn,nice
%O 1,2
%A _Franklin T. Adams-Watters_, Jun 30 2017
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