A084820 - OEIS

%I #10 Sep 12 2019 10:36:32

%S 1,3,5,7,9,11,13,17,19,21,23,25,27,29,31,33,35,37,39,41,43,47,49,51,

%T 53,55,57,59,61,65,67,69,71,73,77,79,81,83,85,87,89,91,93,95,97,99,

%U 101,103,107,109,111,113,115,117,119,121,123,125,127,129,131,133,137

%N Numbers n such that n, sigma(n) and phi(n) form an integer triangle, where sigma=A000203 is the divisor sum and phi=A000010 the totient.

%C a(n)<=A000203(a(n))+A000010(a(n)), A000203(a(n))<=a(n)+A000010(a(n)), A000010(a(n))<=a(n)+A000203(a(n)); values are odd, see A084821 for odd numbers which are not in the sequence.

%H Amiram Eldar, <a href="/A084820/b084820.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>

%e n=5, a(5)=9: phi(9)=6, sigma(9)=13: (6,9,13)=(A070080(176), A070081(176), A070082(176)).

%t Select[Range[1, 140, 2], DivisorSigma[1, #] < EulerPhi[#] + # &] (* _Amiram Eldar_, Sep 12 2019 *)

%o (PARI) is(n)=eulerphi(n)+n>sigma(n) \\ _Charles R Greathouse IV_, Feb 19 2013

%Y Cf. A046022.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jun 04 2003