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%I #25 Feb 14 2021 20:41:42
%S 124,378,403,1904,3751,4064,5187,5456,6188,9296,9800,11532,12369,
%T 13664,14378,15210,16256,16352,17654,18018,18536,19110,19304,19376,
%U 20336,21450,22971,23240,23478,24056,24584,24986,25298,26754,28616,28938,31640,33883,34398
%N Numbers k such that card({x|sigma(x)=k}) > 1 and (Sum_{sigma(x)=k} x) < k.
%C By definition these terms do not belong to A007370 nor to A007369.
%C All terms so far appear to be in A007371, with 2 pre-images. Are there any terms with more?
%C Yes, I find six up to 10^8 with 3 pre-images: 10714158, 12093224, 17315298, 30507906, 54891018, 81629262. - _Charles R Greathouse IV_, Jun 15 2015
%H Charles R Greathouse IV, <a href="/A258931/b258931.txt">Table of n, a(n) for n = 1..10000</a>
%e For k=124, the x's such that sigma(x)=124 are 48 and 75, and 48 + 75 = 123 < 124.
%o (PARI) isok(n) = my(v = select(x->sigma(x)==n, vector(n, i, i))); (#v > 1) && (vecsum(v) < n);
%o (PARI) list(lim)=my(v=vector(lim\1), u=List(), s); for(k=1,#v,s=sigma(k); if(s>#v,next); v[s]=if(v[s]==0, -k, abs(v[s])+k)); for(i=1,#v, if(v[i]>0 && v[i]<i, listput(u,i))); Vec(u) \\ _Charles R Greathouse IV_, Jun 15 2015
%Y Subsequence of A159886.
%Y Cf. A000203 (sigma, the sum of divisors), A085790.
%Y Cf. A007369 (sigma(x)=n has no solution), A007370 (exactly 1 solution),
%Y Cf. A007371 (exactly 2 solutions), A007372 (exactly has 3 solutions).
%Y Cf. A258913 (sum(x|sigma(x)=n).
%K nonn
%O 1,1
%A _Michel Marcus_, Jun 15 2015
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