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.

Showing 1-10 of 11 results. Next

A160321 Numbers n for which sigma(n)/n=k+2/3 with integer k.

Original entry on oeis.org

84, 270, 1488, 1638, 24384, 35640, 199584, 2142720, 12999168, 100651008, 208565280, 240589440, 470564640, 3899750400, 6039429120, 25769607168, 36639203328, 53798734080, 231758392320, 314039721600, 412316073984, 5566503720960, 5967138078720, 302512616524800
Offset: 1

Views

Author

J.C.Klein (hklein(AT)planet.nl), May 08 2009

Keywords

Examples

			84 is in the sequence because sigma(84)/84=224/84=2+2/3
270 is in the sequence because sigma(270)/270=720/270=2+2/3

Crossrefs

Cf. A160320 (sigma(n)/n=k+1/3), A159907 (sigma(n)/n=k+1/2).

Extensions

a(10)-a(18) from Donovan Johnson, May 26 2009
a(19)-a(24) from Michel Marcus, Sep 21 2012

A245775 Numbers k such that A017666(k) = denominator(sigma(k)/k) = 3.

Original entry on oeis.org

3, 12, 84, 234, 270, 1080, 1488, 1638, 6048, 6552, 24384, 35640, 199584, 435708, 2142720, 4713984, 12999168, 18506880, 36197280, 100651008, 208565280, 240589440, 275890944, 299980800, 470564640, 3899750400, 4138364160, 6039429120, 13286744064, 17827568640
Offset: 1

Views

Author

Jaroslav Krizek, Aug 26 2014

Keywords

Comments

Numbers n such that sigma(n)/n = k + 1/3 with integer k are terms of this sequence (3, 12, 234, 1080, 6048, 6552, 435708, 4713984, ...).
Subsequence of A245774 (numbers n such that n divides 3*sigma(n)).
Union of A160320 (sigma(n)/n = k + 1/3) and A160321 (sigma(n)/n = k + 2/3). - Michel Marcus, Aug 27 2014

Examples

			Number 12 is in sequence because A017666(12) = 3.

Links

Crossrefs

Cf. A000203, A007691, A160320, A160321, A245774.

Programs

  • Magma
    [n: n in [1..3000000] | Denominator((SumOfDivisors(n))/n) eq 3]
  • PARI
    for(n=1,10^7,if(denominator(sigma(n)/n)==3,print1(n,", "))) \\ Derek Orr, Aug 26 2014

Extensions

More terms from A160320 and A160321 by Michel Marcus, Aug 27 2014

A218416 Numbers k for which sigma(k)/k - 5/9 is an integer.

Original entry on oeis.org

117, 3780, 66960, 167400, 406224, 1097280, 6656832, 13035330, 29410290, 4529295360, 27477725184, 88071903612, 1159632322560, 7035102756864, 18554223329280, 22385029489560, 54934276752360, 112562288197632, 125356165141536, 307631949813216, 1317932346931200
Offset: 1

Views

Author

Zdenek Cervenka, Oct 28 2012

Keywords

Comments

a(13) > 10^11. - Donovan Johnson, Nov 01 2012
a(13) > 10^12. - Giovanni Resta, Nov 04 2012
Note that there are no terms here with abundancy 23/9 (k=2). - Michel Marcus, Jun 25 2013

Crossrefs

Cf. A218414, A218430, A160320, A218415, A160321, A218417, A218418.

Extensions

a(10)-a(12) from Donovan Johnson, Nov 01 2012
More terms from Michel Marcus, Jun 25 2013

A218414 Numbers k for which sigma(k)/k - 1/9 is an integer.

Original entry on oeis.org

540, 3276, 58032, 950976, 1862190, 17660160, 3925389312, 1005014679552, 16080326885376, 17908023591648, 43947421401888, 92069057203200, 207726054681600, 411471933675264, 12363050673792000, 160893693946908502272, 269783631952374398976, 467406267507560908800
Offset: 1

Views

Author

Zdenek Cervenka, Oct 28 2012

Keywords

Comments

a(8) > 10^11. - Donovan Johnson, Nov 01 2012
a(8) > 10^12. - Giovanni Resta, Nov 04 2012
Note that there are no terms with abundancy 10/9 (k=1) or 19/9 (k=2). Michel Marcus, Jun 25 2013

Crossrefs

Cf. A218430, A160320, A218415, A218416, A160321, A218417, A218418.

Extensions

a(6)-a(7) from Donovan Johnson, Nov 01 2012
More terms from Michel Marcus, Jun 25 2013

A218415 Numbers k for which sigma(k)/k - 4/9 is an integer.

Original entry on oeis.org

9, 1782, 2160, 5400, 13104, 52141320, 117641160, 173365920, 6829038720, 12415092480, 13356796320, 104381747712, 513480135168, 1377031864320, 6578372828160, 26896578508800, 294208373809152, 1447285170659328, 3151812152130048, 7734746166732288
Offset: 1

Views

Author

Zdenek Cervenka, Oct 28 2012

Keywords

Comments

a(12) > 10^11. - Donovan Johnson, Nov 01 2012
a(14) > 10^12. - Giovanni Resta, Nov 04 2012

Crossrefs

Cf. A218414, A218430, A160320, A218416, A160321, A218417, A218418.

Extensions

a(6)-a(11) from Donovan Johnson, Nov 01 2012
a(12)-a(13) from Giovanni Resta, Nov 04 2012
More terms from Michel Marcus, Jun 25 2013

A218417 Numbers k for which sigma(k)/k - 7/9 is an integer.

Original entry on oeis.org

135, 216, 819, 2678400, 6780874383360, 15298997575680, 358160471832960, 878948428037760, 69640897897267200, 27548836016065625124864000, 114509071123027415138304000, 204540330952262537736192000, 32445066814696289084018688000, 42000317261222229165905510400
Offset: 1

Views

Author

Zdenek Cervenka, Oct 28 2012

Keywords

Comments

a(5) > 10^11. - Donovan Johnson, Nov 01 2012
a(5) > 10^12. - Giovanni Resta, Nov 04 2012

Crossrefs

Cf. A218414, A218430, A160320, A218415, A218416, A160321, A218418.

Extensions

More terms from Michel Marcus, Jun 26 2013

A218418 Numbers k for which sigma(k)/k - 8/9 is an integer.

Original entry on oeis.org

252, 4464, 73152, 7448760, 41713056, 48117888, 94112928, 301953024, 975576960, 1773584640, 10759746816, 46351678464, 77308821504, 103448378880, 196718837760, 233400061440, 409698051840, 939767546880
Offset: 1

Views

Author

Zdenek Cervenka, Oct 28 2012

Keywords

Comments

a(14) > 10^11. - Donovan Johnson, Nov 01 2012
a(19) > 10^12. - Giovanni Resta, Nov 04 2012

Crossrefs

Cf. A218414, A218430, A160320, A218415, A218416, A160321, A218417.

Extensions

a(5)-a(13) from Donovan Johnson, Nov 01 2012
a(14)-a(18) from Giovanni Resta, Nov 04 2012

A218430 Numbers k for which sigma(k)/k - 2/9 is an integer.

Original entry on oeis.org

54, 2744280, 6191640, 182494620, 653425920, 702989280, 27025270272, 72475361280, 76172903718912, 15224461545984768, 1688635722988634112, 5953066676035614584064, 1608903162935227680030720, 14600472124349965895417376, 2263986000385276007625523200
Offset: 1

Views

Author

Zdenek Cervenka, Oct 28 2012

Keywords

Comments

a(9) > 10^11. - Donovan Johnson, Nov 01 2012
a(9) > 10^12. - Giovanni Resta, Nov 04 2012
Note that there are no terms here with abundancy 11/9 (k=1) or 29/9 (k=3). - Michel Marcus, Jun 25 2013

Crossrefs

Cf. A218414, A160320, A218415, A218416, A160321, A218417, A218418.

Extensions

a(4)-a(8) from Donovan Johnson, Nov 01 2012
More terms from Michel Marcus, Jun 25 2013

A227303 Numbers k such that k divides sigma(3*k).

Original entry on oeis.org

1, 2, 4, 28, 40, 78, 90, 224, 360, 496, 546, 2016, 2184, 8128, 10080, 10920, 11880, 66528, 145236, 174592, 714240, 726180, 1571328, 4333056, 6168960, 7856640, 12065760, 15177600, 33550336, 47663616, 69521760, 80196480, 91963648, 99993600, 156854880, 459818240, 492101632
Offset: 1

Views

Author

Alex Ratushnyak, Jul 05 2013

Keywords

Comments

If k belongs to the sequence, then sigma(3*k)/k is an integer, so sigma(3*k)/(3*k) is either an integer or a third of an integer, so 3*k is either multiperfect or belongs to A160320 or A160321. - Michel Marcus, Jul 09 2013

Links

Crossrefs

Cf. A000203, A007691, A227302.
Cf. A160320, A160321.

Programs

  • Mathematica
    k = 0; lst = {}; While[k < 10^11, If[ Mod[ DivisorSigma[1, 3 k], k] == 0, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Mar 07 2021 *)
  • PARI
    isok(k) = !(sigma(3*k) % k); \\ Michel Marcus, Mar 07 2021

A364976 3-abundant numbers k such that k/(sigma(k)-3*k) is an integer.

Original entry on oeis.org

180, 240, 360, 420, 540, 600, 780, 1080, 1344, 1872, 1890, 2016, 2184, 2352, 2376, 2688, 3192, 3276, 3744, 4284, 4320, 4680, 5292, 5376, 5796, 6048, 6552, 7128, 7440, 8190, 10416, 13776, 14850, 18600, 19824, 19872, 20496, 21528, 22932, 25056, 26208, 26496, 26784
Offset: 1

Views

Author

Amiram Eldar, Aug 15 2023

Keywords

Comments

Analogous to A153501 as 3-abundant numbers (A068403) are analogous to abundant numbers (A005101).
Numbers k such that the sum of the divisors of k except for one of them is equal to 3*k.

Examples

			180 is a term since sigma(180) - 3*180 = 6 > 0 and 180 is divisible by 6.

Links

Crossrefs

Subsequence of A068403.
A027687 is a subsequence.
Cf. A000203 (sigma), A005101, A005820, A055153, A153501, A160320, A218404, A218406, A329189, A364977.

Programs

  • Mathematica
    Select[Range[27000], (d = DivisorSigma[1, #] - 3*#) > 0 && Divisible[#, d] &]
  • PARI
    is(n) = {my(d = sigma(n) - 3*n); d > 0 && n%d == 0;}
Showing 1-10 of 11 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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