

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
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OFFSET

1,2


COMMENTS

A161788(a(n)) = A161789(a(n)) = 1.
Numbers which are not multiple of 2^k1, k > 1. Because 2^k1 = 1+2+...+2^(k1), 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).  JeanChristophe HervĂ©, 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^k1, {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



