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 1-3 of 3 results.

A138171 Odd n where d(n) > d(n+1), where d(n) = number of positive divisors of n.

Original entry on oeis.org

45, 81, 105, 117, 165, 225, 261, 273, 297, 315, 325, 333, 345, 357, 385, 405, 435, 441, 465, 477, 495, 513, 525, 555, 561, 567, 585, 595, 621, 625, 627, 651, 675, 693, 705, 715, 765, 777, 795, 801, 825, 837, 855, 861, 885, 891, 897, 915, 925, 945, 957, 975
Offset: 1

Views

Author

Leroy Quet, Mar 03 2008

Keywords

Comments

Terms calculated by M. F. Hasler.
First term == 5 (mod 6) is a(385) = 6125. - Jianing Song, Apr 03 2018

Links

Crossrefs

Cf. A138046, A138172.

Programs

  • GAP
    Filtered([1,3..1301],n->Tau(n)>Tau(n+1)); # Muniru A Asiru, Apr 05 2018
  • Maple
    with(numtheory): a:=proc(n) if tau(2*n)Emeric Deutsch, Mar 12 2008
with(numtheory): a:=proc (n) if `mod`(n,2)=1 and tau(n+1) < tau(n) then n else end if end proc: seq(a(n), n=1..1000); # Emeric Deutsch, Mar 31 2008
  • Mathematica
    Select[Range[1,1001,2],DivisorSigma[0,#]>DivisorSigma[0,#+1]&] (* Harvey P. Dale, Jul 08 2017 *)
Select[Flatten[Position[Partition[DivisorSigma[0,Range[1000]],2,1],?(#[[1]]>#[[2]]&),1,Heads->False]],OddQ] (* _Harvey P. Dale, Apr 20 2025 *)
  • PARI
    isok(n) = (n%2) && (numdiv(n) > numdiv(n+1)); \\ Michel Marcus, Apr 04 2018
  • PARI
    lista(nn) = forstep(n=1, nn, 2, if(numdiv(n) > numdiv(n+1), print1(n, ", "))); \\ Altug Alkan, Apr 04 2018

A138172 Even n where d(n) < d(n+1), where d(n) = number of positive divisors of n.

Original entry on oeis.org

62, 74, 134, 146, 164, 188, 194, 206, 254, 274, 278, 284, 314, 356, 362, 386, 398, 404, 422, 428, 454, 458, 482, 494, 524, 538, 554, 566, 584, 614, 626, 662, 674, 692, 734, 746, 758, 764, 794, 818, 824, 854, 866, 890, 914, 926, 934, 944, 956, 974, 998, 1004, 1028
Offset: 1

Views

Author

Leroy Quet, Mar 03 2008

Keywords

Comments

Terms calculated by M. F. Hasler.
First term == 0 (mod 6) is a(133) = 2274. - Jianing Song, Apr 03 2018

Links

Crossrefs

Cf. A000005, A138046, A138171.

Programs

A138047 Positive integers n such that (d(n+1) - d(n)) * (-1)^n is nonnegative, where d(n) = the number of positive divisors of n.

Original entry on oeis.org

2, 14, 21, 26, 33, 34, 38, 44, 45, 57, 62, 74, 75, 81, 85, 86, 93, 94, 98, 104, 105, 116, 117, 118, 122, 133, 134, 135, 141, 142, 145, 146, 147, 158, 164, 165, 171, 177, 188, 189, 194, 201, 202, 205, 206, 213, 214, 217, 218, 225, 230, 231, 242, 243, 244, 253
Offset: 1

Views

Author

Leroy Quet, Mar 02 2008

Keywords

Crossrefs

Cf. A138046, A005237.

Programs

  • Maple
    with(numtheory): a:=proc(n) if 0<=(-1)^n*(tau(n+1)-tau(n)) then n else end if end proc: seq(a(n),n=1..240); # Emeric Deutsch, Mar 06 2008
A051950 := proc(n) numtheory[tau](n)-numtheory[tau](n+1) ; end: A138047 := proc(n) option remember ; local a; if n = 1 then 2 ; else for a from A138047(n-1)+1 do if (-1)^a*A051950(a+1) >= 0 then RETURN(a) ; fi ; od: fi ; end: seq(A138047(n),n=1..80) ; # R. J. Mathar, Mar 31 2008
  • Mathematica
    Select[Range[500], (DivisorSigma[0, # + 1] - DivisorSigma[0, # ])*(-1)^# > -1 &] (* Stefan Steinerberger, Mar 03 2008 *)

Formula

Union of the terms of A138046 and A005237.

Extensions

More terms from Stefan Steinerberger and Emeric Deutsch, Mar 03 2008
More terms from R. J. Mathar, Mar 31 2008
Showing 1-3 of 3 results.

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