cp's OEIS Frontend

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

%I A138171 #24 Apr 20 2025 17:48:02
%S A138171 45,81,105,117,165,225,261,273,297,315,325,333,345,357,385,405,435,
%T A138171 441,465,477,495,513,525,555,561,567,585,595,621,625,627,651,675,693,
%U A138171 705,715,765,777,795,801,825,837,855,861,885,891,897,915,925,945,957,975
%N A138171 Odd n where d(n) > d(n+1), where d(n) = number of positive divisors of n.
%C A138171 Terms calculated by _M. F. Hasler_.
%C A138171 First term == 5 (mod 6) is a(385) = 6125. - _Jianing Song_, Apr 03 2018
%H A138171 Harvey P. Dale, <a href="/A138171/b138171.txt">Table of n, a(n) for n = 1..1000</a>
%p A138171 with(numtheory): a:=proc(n) if tau(2*n)<tau(2*n-1) then 2*n-1 else end if end proc: seq(a(n),n=1..500); # _Emeric Deutsch_, Mar 12 2008
%p A138171 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
%t A138171 Select[Range[1,1001,2],DivisorSigma[0,#]>DivisorSigma[0,#+1]&] (* _Harvey P. Dale_, Jul 08 2017 *)
%t A138171 Select[Flatten[Position[Partition[DivisorSigma[0,Range[1000]],2,1],_?(#[[1]]>#[[2]]&),1,Heads->False]],OddQ] (* _Harvey P. Dale_, Apr 20 2025 *)
%o A138171 (PARI) isok(n) = (n%2) && (numdiv(n) > numdiv(n+1)); \\ _Michel Marcus_, Apr 04 2018
%o A138171 (PARI) lista(nn) = forstep(n=1, nn, 2, if(numdiv(n) > numdiv(n+1), print1(n, ", "))); \\ _Altug Alkan_, Apr 04 2018
%o A138171 (GAP) Filtered([1,3..1301],n->Tau(n)>Tau(n+1)); # _Muniru A Asiru_, Apr 05 2018
%Y A138171 Cf. A138046, A138172.
%K A138171 nonn
%O A138171 1,1
%A A138171 _Leroy Quet_, Mar 03 2008