A067828 Odd numbers k such that sigma(k+1) < sigma(k).

45, 105, 117, 165, 225, 273, 297, 315, 345, 357, 405, 465, 513, 525, 561, 585, 621, 693, 705, 765, 777, 825, 837, 861, 885, 945, 1005, 1113, 1125, 1155, 1185, 1197, 1281, 1305, 1365, 1395, 1425, 1485, 1521, 1545, 1575, 1593, 1617, 1701, 1725, 1755, 1785, 1845

Offset: 1

Author

Benoit Cloitre, Feb 08 2002

Keywords

• nonn

Comments

Most terms are == 3 (mod 6), first term == 1 (mod 6) is a(130) = 5005. First term == 5 (mod 6) may be 247818996425. - Jianing Song, Apr 01 2018

Links

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

Crossrefs

Cf. A000203, A053224, A067825.

Programs

Mathematica

Select[Range[1, 2000, 2], DivisorSigma[1, #] > DivisorSigma[1, # + 1] &] (* Amiram Eldar, Jun 06 2022 *)
Select[Flatten[Position[Partition[DivisorSigma[1,Range[2000]],2,1],?(#[[2]]<#[[1]]&),1,Heads-> False]],OddQ] (* _Harvey P. Dale, Aug 02 2024 *)

PARI

isok(n) = (n % 2) && (sigma(n+1) < sigma(n)); \\ Michel Marcus, Nov 23 2013