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 1-5 of 5 results.

A364657 Numbers k such that sigma(k) > sigma(k+1) > sigma(k+2).

Original entry on oeis.org

44, 45, 104, 105, 116, 117, 164, 165, 224, 225, 272, 273, 296, 297, 315, 344, 345, 356, 357, 405, 464, 465, 512, 513, 525, 560, 561, 584, 585, 620, 621, 693, 704, 705, 765, 776, 777, 824, 825, 836, 837, 860, 861, 884, 885, 945, 1004, 1005, 1112, 1113, 1125, 1155
Offset: 1

Views

Author

Seiichi Manyama, Aug 01 2023

Keywords

Links

Crossrefs

Cf. A050944, A053226, A364659.

Programs

  • PARI
    isok(n) = sigma(n)>sigma(n+1) && sigma(n+1)>sigma(n+2);

A364662 Numbers k such that sigma(k) < sigma(k+1) < sigma(k+2) < sigma(k+3).

Original entry on oeis.org

1, 61, 73, 133, 145, 193, 253, 397, 457, 481, 493, 553, 565, 613, 625, 661, 673, 733, 757, 793, 817, 853, 913, 973, 997, 1033, 1093, 1213, 1237, 1285, 1321, 1453, 1513, 1537, 1645, 1657, 1681, 1813, 1825, 1873, 1933, 2077, 2113, 2173, 2233, 2245, 2293, 2413, 2497, 2533, 2581, 2593, 2653, 2713
Offset: 1

Views

Author

Seiichi Manyama, Aug 01 2023

Keywords

Links

Crossrefs

Cf. A050944, A053224, A364659.

Programs

  • PARI
    isok(n) = sigma(n)

A364719 Numbers k such that d(k) > d(k+1) > d(k+2) > d(k+3), where d(n) is the number of divisors of n.

Original entry on oeis.org

80, 224, 260, 440, 464, 476, 560, 594, 650, 714, 836, 860, 884, 980, 1016, 1088, 1184, 1280, 1376, 1520, 1700, 1862, 1904, 2024, 2060, 2096, 2444, 2450, 2816, 2870, 2960, 2996, 3020, 3024, 3164, 3200, 3320, 3380, 3450, 3620, 3800, 3944, 3968, 4004, 4130, 4136, 4250
Offset: 1

Views

Author

Seiichi Manyama, Aug 04 2023

Keywords

Links

Crossrefs

Cf. A000005, A050944, A075029.
Cf. A074827, A364718, A364720.

Programs

  • Mathematica
    Flatten@Position[Differences@#&/@Partition[DivisorSigma[0,Range@5000],4,1], {?(#<0&)..}] (* _Hans Rudolf Widmer, Mar 11 2024 *)
  • PARI
    isok(n) = numdiv(n)>numdiv(n+1) && numdiv(n+1)>numdiv(n+2) && numdiv(n+2)>numdiv(n+3);

A050945 Numbers k such that sigma(k) > sigma(k+1) > sigma(k+2) > sigma(k+3) > sigma(k+4) > sigma(k+5).

Original entry on oeis.org

20021154, 28503474, 53728674, 224539314, 242917674, 304178874, 341295954, 370845474, 377692314, 443998554, 533007474, 610484874, 709445274, 855529674, 964885074, 978052074, 1069943874, 1114988874, 1167961794
Offset: 1

Views

Author

Jud McCranie, Jan 02 2000

Keywords

Comments

There are many examples of 4 consecutive numbers having decreasing values of sigma (see cross references) and there are 83 cases of 6 consecutive numbers with decreasing values of sigma < 4,293,000,000. Interestingly (and for unknown reasons) there are no examples of exactly 5 such consecutive numbers in that range! All known members of the sequence are multiples of 6 and one less than a multiple of 35.

Examples

			sigma(20021154)=40894848 > sigma(20021155)=35458560 > ... > sigma(20021159)=20021160.

References

  • David Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 44.

Links

Crossrefs

Cf. A000203, A050944, A053226, A364657, A364680.

Extensions

Name simplified by Seiichi Manyama, Aug 03 2023

A364680 Smallest initial number k of n consecutive numbers satisfying sigma(k) > sigma(k+1) > ... > sigma(k+n-1).

Original entry on oeis.org

1, 4, 44, 44, 20021154, 20021154
Offset: 1

Views

Author

Seiichi Manyama, Aug 02 2023

Keywords

Crossrefs

Cf. A000203, A075029.
Cf. A050944, A050945, A053226, A364657.

Programs

  • PARI
    b(n) = my(k=n); while(sigma(k)>sigma(k+1), k++); k-n+1;
a(n) = my(k=1); while(b(k)
Showing 1-5 of 5 results.

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

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