A161790 - OEIS

%I #40 Feb 11 2020 02:05:07

%S 1,2,4,5,8,10,11,13,16,17,19,20,22,23,25,26,29,32,34,37,38,40,41,43,

%T 44,46,47,50,52,53,55,58,59,61,64,65,67,68,71,73,74,76,79,80,82,83,85,

%U 86,88,89,92,94,95,97,100,101,103,104,106,107,109,110,113,115,116,118,121,122,125,128,130,131,134,136,137,139,142,143

%N The positive integer n is included if 1 is the largest integer of the form {2^k - 1} to divide n.

%C A161788(a(n)) = A161789(a(n)) = 1.

%C Numbers which are not multiple of 2^k-1, k > 1. Because 2^k-1 = 1+2+...+2^(k-1), these numbers are also not the sum of positive integers in a geometric progression with common ratio 2 (cf. the primes A000040 which satisfy a similar property with arithmetic progressions with common difference 2). - _Jean-Christophe Hervé_, Jun 19 2014

%C Also A154402(a(n)) = 1. - _Antti Karttunen_, Jun 11 2018

%H Diana L. Mecum, <a href="/A161790/b161790.txt">Table of n, a(n) for n = 1..2000</a>

%t DivisorList=Drop[Table[2^k-1,{k,1,20}],1]

%t A161790=Union[Table[If[Length[Join[DivisorList,Drop[Divisors[n],1]]]==Length[Union[DivisorList,Drop[Divisors[n],1]]],n,],{n,1,5000}]]

%t (* Second program: *)

%t Position[Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# + 1] &], {n, 143}], 1][[All, 1]] (* _Michael De Vlieger_, Jun 11 2018 *)

%Y Cf. A000225.

%Y Positions of ones in A154402, A161788 and A161789.

%K nonn

%O 1,2

%A _Leroy Quet_, Jun 19 2009