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A293542 a(1)=1; for n>1, a(n) = least integer greater than a(n-1) such that the sums of the divisors of the pairwise sums of a(1),...,a(n) are all distinct.

%I A293542 #9 Oct 13 2017 09:12:14
%S A293542 1,2,4,8,19,28,56,72,101,144,202,240,261,448,511,602,772,806,1152,
%T A293542 1296,1541,1602,2016,2256,2900,3322,3362,3978,4376,5887,6416,7702,
%U A293542 8228,8578,11341,11382,13376,13692,16083,16380,16544,17382,22726,24944,26302,27508,30580,33184,34020,37474
%N A293542 a(1)=1; for n>1, a(n) = least integer greater than a(n-1) such that the sums of the divisors of the pairwise sums of a(1),...,a(n) are all distinct.
%H A293542 Logan J. Kleinwaks, <a href="/A293542/b293542.txt">Table of n, a(n) for n = 1..250</a>
%e A293542 Let s(n) be the sum of the divisors of n. a(3)!=3 because s(1+3)=s(2+2)=7. a(3)=4 because s(1+1)=3, s(1+2)=4, s(1+4)=6, s(2+2)=7, s(2+4)=12, and s(4,4)=15 are all distinct.
%Y A293542 Cf. A000203, A293541, A005282.
%K A293542 nonn
%O A293542 1,2
%A A293542 _Logan J. Kleinwaks_, Oct 11 2017