A258931 Numbers k such that card({x|sigma(x)=k}) > 1 and (Sum_{sigma(x)=k} x) < k.

124, 378, 403, 1904, 3751, 4064, 5187, 5456, 6188, 9296, 9800, 11532, 12369, 13664, 14378, 15210, 16256, 16352, 17654, 18018, 18536, 19110, 19304, 19376, 20336, 21450, 22971, 23240, 23478, 24056, 24584, 24986, 25298, 26754, 28616, 28938, 31640, 33883, 34398

Offset: 1

Author

Michel Marcus, Jun 15 2015

Keywords

• nonn

Comments

By definition these terms do not belong to A007370 nor to A007369.

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

Examples

			For k=124, the x's such that sigma(x)=124 are 48 and 75, and 48 + 75 = 123 < 124.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A159886.

Cf. A000203 (sigma, the sum of divisors), A085790.

Cf. A007369 (sigma(x)=n has no solution), A007370 (exactly 1 solution),

Cf. A007371 (exactly 2 solutions), A007372 (exactly has 3 solutions).

Cf. A258913 (Sum_{sigma(x)=n} x).

Programs

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]Charles R Greathouse IV, Jun 15 2015