cp's OEIS Frontend

A161790 The positive integer n is included if 1 is the largest integer of the form {2^k - 1} to divide n.

%I A161790 #48 Jun 30 2025 04:26:35
%S A161790 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 A161790 44,46,47,50,52,53,55,58,59,61,64,65,67,68,71,73,74,76,79,80,82,83,85,
%U A161790 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 A161790 The positive integer n is included if 1 is the largest integer of the form {2^k - 1} to divide n.
%C A161790 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 A161790 The asymptotic density of this sequence is 1 - Sum_{s subset of A000225 \ {0, 1}} (-1)^(card(s)+1)/LCM(s) = 0.54830... - _Amiram Eldar_, Jun 30 2025
%H A161790 Diana L. Mecum, <a href="/A161790/b161790.txt">Table of n, a(n) for n = 1..2000</a>
%F A161790 A161788(a(n)) = A161789(a(n)) = 1.
%F A161790 Also A154402(a(n)) = 1. - _Antti Karttunen_, Jun 11 2018
%t A161790 DivisorList=Drop[Table[2^k-1,{k,1,20}],1]
%t A161790 A161790=Union[Table[If[Length[Join[DivisorList,Drop[Divisors[n],1]]]==Length[Union[DivisorList,Drop[Divisors[n],1]]],n,],{n,1,5000}]]
%t A161790 (* Second program: *)
%t A161790 Position[Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# + 1] &], {n, 143}], 1][[All, 1]] (* _Michael De Vlieger_, Jun 11 2018 *)
%o A161790 (PARI) isok(k) = forstep(i = logint(k+1, 2), 2, -1, if(k % (2^i-1) == 0, return(0))); 1; \\ _Amiram Eldar_, Jun 30 2025
%Y A161790 Cf. A000225, A382875 (complement).
%Y A161790 Positions of ones in A154402, A161788 and A161789.
%K A161790 nonn
%O A161790 1,2
%A A161790 _Leroy Quet_, Jun 19 2009