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%I #19 Jul 16 2021 03:31:20
%S 6,15,21,33,39,51,57,69,87,93,111,123,129,141,159,175,177,183,201,213,
%T 219,237,249,267,291,303,309,321,327,339,381,393,411,417,447,453,471,
%U 489,501,519,537,543,573,579,591,597,633,669,681,687,699,717,723,753
%N Numbers k such that 2*phi(k) + 8 = sigma(k).
%C For 16 < n < 10^8, a(n) = 3*prime(n). Note also that a(n) is odd for n > 1. - _Charles R Greathouse IV_, Nov 19 2015
%H Harry J. Smith, <a href="/A063466/b063466.txt">Table of n, a(n) for n = 1..10000</a>
%e If p is a prime other than 3, 2*phi(3p) = 2(2p-2) = 4p - 4, sigma(3p) = 4p + 4, 2*phi(3p) + 8 = sigma(3p). So numbers of the form 3p are in the sequence. Also if k=175, phi(175) = 120, sigma(175) = 248, thus 2*phi(175) + 8 = sigma(175), so 175 is here. Note that 175 is not of the form 3p. No additional terms not of the form 3p were found below 100000.
%t Select[Range[800],2*EulerPhi[#]+8==DivisorSigma[1,#]&] (* _Harvey P. Dale_, Dec 28 2017 *)
%o (PARI) n=-1; for (m=1, 10^9, if (sigma(m) - 2*eulerphi(m) == 8, write("b063466.txt", n++, " ", m); if (n==1000, break))) \\ _Harry J. Smith_, Aug 22 2009
%o (PARI) is(n)=my(f=factor(n)); 2*eulerphi(f)+8 == sigma(f) \\ _Charles R Greathouse IV_, Nov 19 2015
%Y Cf. A000010, A000203.
%K nonn
%O 1,1
%A _Labos Elemer_, Jul 26 2001