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

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

Author

Leroy Quet, Mar 03 2008

Keywords

• nonn

Comments

Terms calculated by M. F. Hasler.

First term == 5 (mod 6) is a(385) = 6125. - Jianing Song, Apr 03 2018

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

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