A295584 Odd numbers that are not a product of Mersenne numbers (A000225).

5, 11, 13, 17, 19, 23, 25, 29, 33, 35, 37, 39, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 69, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 129, 131, 133, 137, 139, 141, 143, 145, 149, 151, 153

Offset

1,1

Comments

Numbers m such that no commutative ring has m units.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

S. Chebolu and K. Lockridge, How Many Units Can a Commutative Ring Have?, Amer. Math. Monthly, 124 (2017), 960-965; arXiv, arXiv:1701.02341 [math.AC], 2017.

Maple

N:= 1000: # to get all terms <= N
P:= {1}:
for k from 2 do
  m:= 2^k-1;
  if m > N then break fi;
  P:= map(p -> seq(p*m^j, j=0..floor(log[m](N/p))), P);
od:
sort(convert({seq(i, i=1..N, 2)} minus P, list)); # Robert Israel, Dec 15 2017

Mathematica

nn == 1000;
P = {1};
For[k = 2, True, k++,
   m = 2^k - 1;
   If[m > nn, Break[]
];
P = (Function[p, Table[p m^j, {j, 0, Log[m, nn/p]}]] /@ P) // Flatten];
Range[1, nn, 2] ~Complement~ P (* Jean-François Alcover, Sep 18 2018, after Robert Israel *)

Crossrefs

Odd numbers not in A282572; complement of A296241.

Cf. A000225.

Sequence in context: A337658 A206548 A206547 * A185208 A216227 A020611

Adjacent sequences: A295581 A295582 A295583 * A295585 A295586 A295587

Keyword

nonn

Author

N. J. A. Sloane, Dec 15 2017

Status

approved