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A258931 Numbers k such that card({x|sigma(x)=k}) > 1 and (Sum_{sigma(x)=k} x) < k. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
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
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(x|sigma(x)=n).
Sequence in context: A246732 A214485 A045250 * A204642 A204635 A102589
KEYWORD
nonn
AUTHOR
Michel Marcus, Jun 15 2015
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)