%I
%S 1,2,3,4,7,8,16,21,27,32,36,50,63,64,93,98,100,128,144,256,324,392,
%T 400,512,576,784,800,900,1296,1600,1936,2304,2916,3600,5184,6400,7744,
%U 8100,9216,10404,11664,14400,17424,19600,20736,22500,30276,32400,41616,46656
%N Sequence, starting with 1, of increasing numbers such that both the numerator and the denominator of the abundancy index, sigma(n)/n are strictly increasing.
%C Records of A239972.
%C Recall that the abundancy index of n is defined as sigma(n)/n with sigma(n) being the sum of divisors of n (A000203). The numerators and denominators of the abundancy index can be found in A017665 and A017666.
%C It appears that all terms belong to A014567, numbers such that sigma(n) and n are coprime.
%C Odd terms begin: 1, 3, 7, 21, 27, 63, 93; and no others were found up to 10^7. What is the next odd number, or is 93 the last odd number in the sequence?
%H Michel Marcus, <a href="/A239973/b239973.txt">Table of n, a(n) for n = 1..254</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Abundancy.html">Abundancy</a>
%o (PARI) lista(nn) = {num = 0; den = 0; for (n = 1, nn, ab = sigma(n)/n; nab = numerator(ab); dab = denominator(ab); if ((nab > num) && (dab > den), print1(n, ", "); num = nab; den = dab;););}
%Y Cf. A000203, A017665, A017666, A239972.
%K nonn
%O 1,2
%A _Michel Marcus_, Mar 30 2014
