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A295584
Odd numbers that are not a product of Mersenne numbers (A000225).
1
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 15 2017
STATUS
approved