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

1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20, 22, 23, 25, 26, 29, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 50, 52, 53, 55, 58, 59, 61, 64, 65, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 85, 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

Offset

1,2

Comments

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

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

Also A154402(a(n)) = 1. - Antti Karttunen, Jun 11 2018

Links

Diana L. Mecum, Table of n, a(n) for n = 1..2000

Mathematica

DivisorList=Drop[Table[2^k-1, {k, 1, 20}], 1]
A161790=Union[Table[If[Length[Join[DivisorList, Drop[Divisors[n], 1]]]==Length[Union[DivisorList, Drop[Divisors[n], 1]]], n, ], {n, 1, 5000}]]
(* Second program: *)
Position[Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# + 1] &], {n, 143}], 1][[All, 1]] (* Michael De Vlieger, Jun 11 2018 *)

Crossrefs

Cf. A000225.

Positions of ones in A154402, A161788 and A161789.

Sequence in context: A120685 A284472 A160545 * A131396 A131391 A185392

Adjacent sequences: A161787 A161788 A161789 * A161791 A161792 A161793

Keyword

nonn

Author

Leroy Quet, Jun 19 2009

Status

approved