OFFSET
1,1
COMMENTS
All terms so far appear to be in A007371, with 2 pre-images. Are there any terms with more?
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
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
For k=124, the x's such that sigma(x)=124 are 48 and 75, and 48 + 75 = 123 < 124.
PROG
(PARI) isok(n) = my(v = select(x->sigma(x)==n, vector(n, i, i))); (#v > 1) && (vecsum(v) < n);
(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
KEYWORD
nonn
AUTHOR
Michel Marcus, Jun 15 2015
STATUS
approved