%I #11 Dec 06 2021 03:12:13
%S 13,19,21,25,26,27,31,33,35,36,37,38,39,41,42,43,49,54,55,56,57,61,62,
%T 65,66,67,70,71,73,74,77,78,79,81,82,86,87,88,89,91,93,95,97,100,101,
%U 103,104,105,109,110,111,112,113,114,115,119,122,123,125,127,129
%N Numbers k such that phi(k) = A000010(k) is an abundant number (A005101) and d(k) = A000005(k) is a deficient number (A005100).
%C Sándor (2005) proved that this sequence is infinite by showing that it includes all the numbers of the form 3^(p^2-1) where p is a prime.
%H Amiram Eldar, <a href="/A349762/b349762.txt">Table of n, a(n) for n = 1..10000</a>
%H József Sándor, <a href="https://blngcc.files.wordpress.com/2008/11/jozsel-sandor-selected-chaters-of-geometry-analysis-and-number-theory.pdf">Selected Chapters of Geometry, Analysis and Number Theory</a>, 2005, pp. 132-134.
%e 13 is a term since phi(13) = 12 is an abundant number, sigma(12) = 28 > 2*12 = 24, and d(13) = 2 is a deficient number, sigma(2) = 3 < 2*2 = 4.
%t abQ[n_] := DivisorSigma[1, n] > 2*n; defQ[n_] := DivisorSigma[1, n] < 2*n; q[n_] := abQ[EulerPhi[n]] && defQ[DivisorSigma[0, n]]; Select[Range[150], q]
%Y Cf. A000005, A000010, A005100, A005101, A349758, A349759, A349761.
%Y A164318 is a subsequence.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 29 2021