A382875 Numbers which are a multiple of 2^k - 1 for some k > 1.

0, 3, 6, 7, 9, 12, 14, 15, 18, 21, 24, 27, 28, 30, 31, 33, 35, 36, 39, 42, 45, 48, 49, 51, 54, 56, 57, 60, 62, 63, 66, 69, 70, 72, 75, 77, 78, 81, 84, 87, 90, 91, 93, 96, 98, 99, 102, 105, 108, 111, 112, 114, 117, 119, 120, 123, 124, 126, 127, 129, 132, 133, 135, 138, 140

Offset: 1

Author

Stefano Spezia, Apr 07 2025

Keywords

• nonn

Comments

The asymptotic density of this sequence is Sum_{s subset of A000225 \ {0, 1}} (-1)^(card(s)+1)/LCM(s) = 0.45169 ... . - Amiram Eldar, Jun 30 2025

Crossrefs

Complement of A161790 in A001477.

Cf. A000225, A161788, A161789.

Programs

Mathematica

nmax=140; Complement[Range[0,nmax], Position[Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# + 1] &], {n, nmax}], 1][[All, 1]]] (* after Michael De Vlieger, Jun 11 2018 in A161790 *)

PARI

isok(k) = if(k == 0, 1, forstep(i = logint(k+1, 2), 2, -1, if(k % (2^i-1) == 0, return(1))); 0); \\ Amiram Eldar, Jun 30 2025