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A161790 The positive integer n is included if 1 is the largest integer of the form {2^k - 1} to divide n. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 16:35 EST 2021. Contains 349394 sequences. (Running on oeis4.)