cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A060676 Numbers k such that sigma (x) = k has exactly 12 solutions.

Original entry on oeis.org

1512, 1872, 2352, 3192, 3780, 4104, 4560, 4752, 5880, 6120, 8160, 8424, 8820, 11424, 13056, 15264, 16464, 16704, 17160, 17360, 17760, 18648, 19680, 19800, 20880, 22752, 23616, 24552, 24864, 27432, 30336, 30492, 31200, 32448, 35328
Offset: 1

Views

Author

Robert G. Wilson v, Apr 18 2001

Keywords

Examples

			1512 = sigma(480) = sigma(636) = sigma(736) = sigma(748) = sigma(830) = sigma(902) = sigma(1006) = sigma(1105) = sigma(1255) = sigma(1391) = sigma(1411) = sigma(1511).

Links

Crossrefs

Cf. A000203.
Number of solutions: A007369 (0), A007370 (1), A007371 (2), A007372 (3), A060660 (4), A060661 (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), this sequence (12).

Programs

  • Mathematica
    a = Table[ 0, {50000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 50001, a[ [ s ] ]++ ], {n, 1, 50000} ]; Select[ Range[ 50000 ], a[ [ # ] ] == 12 & ]
Take[Sort[Transpose[Select[Tally[DivisorSigma[1,Range[100000]]],#[[2]] == 12&]][[1]]],50] (* Harvey P. Dale, Jan 18 2013 *)
  • PARI
    is(k) = invsigmaNum(k) == 12 \\ Amiram Eldar, Nov 18 2024, using Max Alekseyev's invphi.gp

A060678 Numbers k such that sigma (x) = k has exactly 11 solutions.

Original entry on oeis.org

576, 1296, 2976, 3168, 3648, 3720, 4788, 4896, 5544, 6300, 9000, 9840, 10656, 11808, 12528, 13020, 13320, 14760, 15456, 16740, 17920, 18288, 18576, 19344, 19840, 20400, 21280, 22800, 23296, 24300, 26712, 26928, 27552, 27936, 28392
Offset: 1

Views

Author

Robert G. Wilson v, Apr 18 2001

Keywords

Examples

			576 = sigma(210) = sigma(282) = sigma(310) = sigma(322) = sigma(345) = sigma(357) = sigma(382) = sigma(385) = sigma(497) = sigma(517) = sigma(527).

Links

Crossrefs

Cf. A000203.
Number of solutions: A007369 (0), A007370 (1), A007371 (2), A007372 (3), A060660 (4), A060661 (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), this sequence (11), A060676 (12).

Programs

  • Mathematica
    a = Table[ 0, {30000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 30001, a[ [ s ] ]++ ], {n, 1, 30000} ]; Select[ Range[ 30000 ], a[ [ # ] ] == 11 & ]
  • PARI
    is(k) = invsigmaNum(k) == 11 \\ Amiram Eldar, Nov 18 2024, using Max Alekseyev's invphi.gp

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

Original entry on oeis.org

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

Views

Author

Michel Marcus, Jun 15 2015

Keywords

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

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
Previous Showing 11-13 of 13 results.

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