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

Author

N. J. A. Sloane, Dec 15 2017

Keywords

• nonn

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.

Crossrefs

Odd numbers not in A282572; complement of A296241.

Cf. A000225.

Programs

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 *)