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 1-8 of 8 results.

A075028 a(1) = 1, then a(n) = the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are in strictly ascending order.

Original entry on oeis.org

1, 1, 61, 61, 11371, 11371, 7392171, 168776043, 1584614377, 38045133481, 30386250649371, 1848289766450821
Offset: 1

Views

Author

Amarnath Murthy, Sep 02 2002

Keywords

Comments

tau(k) < tau(k+1) < ... < tau(k+n-1).
a(11) > 10^12. - Donovan Johnson, Oct 13 2009
a(11) > 10^13. - Giovanni Resta, Jul 25 2013
a(13) > 2.64*10^15. - Jud McCranie, Mar 27 2019

Examples

			a(3) = 61 = a(4) as tau(61) = 2 < tau(62) = 4 < tau(63) = 6 < tau(64) = 7.

Crossrefs

Cf. A075029, A075031.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
a(7)-a(10) from Donovan Johnson, Oct 13 2009
a(11)-a(12) from Jud McCranie, Mar 27 2019

A075031 a(n) is the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are nonincreasing.

Original entry on oeis.org

1, 2, 20, 20, 714, 714, 25550, 90180, 142803, 809300, 27195648, 27195648, 6973441007, 37962822225, 37962822225, 114296059262, 265228019405583, 394047434860662, 2493689139940250
Offset: 1

Views

Author

Amarnath Murthy, Sep 02 2002

Keywords

Comments

tau(k) >= tau(k+1) >= ... >= tau(k+n-1).
Next term is > 2000000. - David Wasserman, May 06 2005
a(17) > 10^12. [Donovan Johnson, Oct 13 2009]
a(20) > 2.64x10^15. - Jud McCranie, Mar 27 2019

Examples

			a(3)=a(4) = 20 as tau(20) > tau(21) = tau(22) > tau(23).

Crossrefs

Cf. A075028, A075029, A075046.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
a(11)-a(16) from Donovan Johnson, Oct 13 2009
a(17)-a(19) from Jud McCranie, Mar 27 2019

A075046 a(n) = the smallest number k such that the number of divisors of the n numbers from k through k+n-1 are in nondescending order.

Original entry on oeis.org

1, 1, 1, 1, 241, 241, 12853, 12853, 234613, 376741, 78312721, 125938261, 4019167441, 16586155153, 35237422882, 1296230533473, 42301168491121, 61118966262061
Offset: 1

Views

Author

Amarnath Murthy, Sep 03 2002

Keywords

Comments

tau(k) <= tau(k+1) <= ... <= tau(k+n-1).
a(16) > 10^12. - Donovan Johnson, Oct 13 2009
a(17) > 10^13. - Giovanni Resta, Apr 12 2017
a(19) > 2.64*10^15. - Jud McCranie, Mar 27 2019
If a(n) > 1, then A013632(a(n)) >= n. Might be useful to help speed up brute force search. - Chai Wah Wu, May 04 2017

Examples

			a(5) = 241 = a(6) as tau(241) = 2 < tau(242) = tau(243) = tau(244) = tau(245) = 6 < tau(246).

Crossrefs

Cf. A075028, A075029, A075031, A045983, A006073, A075044, A055927, A075047.

Programs

  • Mathematica
    k = 1; Do[ While[t = Table[ DivisorSigma[0, i], {i, k, k + n - 1}]; t != Sort[t], k++ ]; Print[k], {n, 1, 11}]

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
a(11) from Robert G. Wilson v, Sep 07 2003
a(12)-a(15) from Donovan Johnson, Oct 13 2009
a(16) from Fred Schneider, Mar 29 2017
a(17)-a(18) from Jud McCranie, Mar 27 2019

A364718 Numbers k such that d(k) > d(k+1) > d(k+2), where d(n) is the number of divisors of n.

Original entry on oeis.org

45, 80, 81, 105, 165, 224, 225, 260, 261, 272, 315, 324, 345, 357, 384, 405, 435, 440, 441, 464, 465, 476, 477, 495, 512, 555, 560, 561, 567, 585, 594, 595, 620, 624, 627, 650, 651, 675, 704, 714, 715, 795, 800, 825, 836, 837, 855, 860, 861, 884, 885, 891, 896, 915
Offset: 1

Views

Author

Seiichi Manyama, Aug 04 2023

Keywords

Links

Crossrefs

Cf. A000005, A075029, A364657.
Cf. A074827, A364719, A364720.

Programs

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

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);

A364720 Numbers k such that d(k) > d(k+1) > d(k+2) > d(k+3) > d(k+4), where d(n) is the number of divisors of n.

Original entry on oeis.org

28974, 28975, 39150, 39444, 39445, 44863, 60775, 64015, 68875, 71995, 75174, 79135, 79848, 79849, 91195, 103615, 113904, 113905, 118825, 126294, 141955, 143143, 148974, 149823, 150955, 154375, 160734, 160735, 160974, 161343, 167824, 171925, 177330, 181194, 181195
Offset: 1

Views

Author

Seiichi Manyama, Aug 04 2023

Keywords

Links

Crossrefs

Cf. A000005, A075029.
Cf. A074827, A364718, A364719.

Programs

  • Mathematica
    Flatten@Position[Differences@# &/@Partition[DivisorSigma[0, Range@1000000],5,1], {?(# < 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) && numdiv(n+3)>numdiv(n+4);

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)

A188598 Numbers k such that d(k-1) > d(k) > d(k+1) where d(k) is the number of divisors of k.

Original entry on oeis.org

46, 81, 82, 106, 166, 225, 226, 261, 262, 273, 316, 325, 346, 358, 385, 406, 436, 441, 442, 465, 466, 477, 478, 496, 513, 556, 561, 562, 568, 586, 595, 596, 621, 625, 628, 651, 652, 676, 705, 715, 716, 796, 801, 826, 837, 838, 856, 861, 862, 885, 886, 892, 897, 916, 925, 946, 976, 981, 982
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 05 2011

Keywords

Comments

A000005(a(n)-1) > A000005(a(n)) > A000005(a(n)+1).

Links

Crossrefs

Cf. A000005, A188631, A075029.

Programs

  • Mathematica
    Select[Range[2, 1000], DivisorSigma[0, # - 1] > DivisorSigma[0, #] > DivisorSigma[0, # + 1] &] (* T. D. Noe, Apr 05 2011 *)

Extensions

Corrected and extended by T. D. Noe, Apr 05 2011
Showing 1-8 of 8 results.

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