A138172 -id:A138172 - cp's OEIS frontend

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

Leroy Quet, Mar 03 2008

nonn

Terms calculated by M. F. Hasler.

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

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

Cf. A138046, A138172.

Filtered([1,3..1301],n->Tau(n)>Tau(n+1)); # Muniru A Asiru, Apr 05 2018

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

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 *)

isok(n) = (n%2) && (numdiv(n) > numdiv(n+1)); \\ Michel Marcus, Apr 04 2018

lista(nn) = forstep(n=1, nn, 2, if(numdiv(n) > numdiv(n+1), print1(n, ", "))); \\ Altug Alkan, Apr 04 2018

A323379 Odd k such that d(k-1) < d(k) and d(k) > d(k+1), d = A000005.

Original entry on oeis.org

165, 315, 357, 405, 495, 525, 555, 567, 585, 627, 675, 693, 765, 795, 825, 855, 891, 915, 945, 957, 975, 1005, 1053, 1071, 1125, 1155, 1173, 1305, 1323, 1365, 1395, 1425, 1485, 1515, 1575, 1617, 1677, 1683, 1725, 1755, 1785, 1815, 1827, 1845, 1911, 1965, 1995

Offset: 1

Jianing Song, Jan 12 2019

nonn

Numbers k such that k is in A138171 and that k-1 is in A138172.
It's often the case that an odd number has fewer divisors than at least one of its adjacent even numbers. This sequence lists the exceptions.
Most terms are congruent to 3 modulo 6. The smallest term congruent to 1 modulo 6 is 2275, and the smallest term congruent to 5 modulo 6 is 6125.

			d(314) = 4, d(315) = 12, d(316) = 6, so 315 is a term.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A075027 and A005408.
Cf. A000005, A138171, A138172.
Similar sequences: A076773, A323380.

q:= k-> k::odd and (d-> d(k-1)d(k+1))(numtheory[tau]):
select(q, [$1..2000])[];  # Alois P. Heinz, Sep 28 2021

Select[Range[3, 2001, 2], (d = DivisorSigma[0, #] & /@ (# + Range[-1,1]))[[2]] > d[[1]] && d[[2]] > d[[3]] &] (* Amiram Eldar, Jul 22 2019 *)

forstep(n=3,2000,2,if(numdiv(n)>numdiv(n-1)&&numdiv(n)>numdiv(n+1), print1(n, ", ")))

cp's OEIS Frontend

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

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A323379 Odd k such that d(k-1) < d(k) and d(k) > d(k+1), d = A000005.

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Maple

Mathematica

PARI