A340269 Numbers k > 1 such that lpf(k)-1 does not divide d-1 for at least one divisor d of k, where lpf(k) is the least prime factor of k (A020639).
35, 55, 77, 95, 115, 119, 143, 155, 161, 175, 187, 203, 209, 215, 221, 235, 245, 247, 253, 275, 287, 295, 299, 319, 323, 329, 335, 355, 371, 377, 385, 391, 395, 403, 407, 413, 415, 437, 455, 473, 475, 493, 497, 515, 517, 527, 533, 535, 539, 551, 559, 575, 581
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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MATLAB
n=300; % gives all terms of the sequence not exceeding n A=[]; for i=2:n lpf=2; while mod(i,lpf)~=0 lpf=lpf+1; end for d=1:i if mod(i,d)==0 && mod(d-1,lpf-1)~=0 A=[A i]; break end end end -
Maple
with(numtheory): q:= n-> (f-> ormap(d-> irem(d-1, f)>0, divisors(n)))(min(factorset(n))-1): select(q, [$2..600])[]; # Alois P. Heinz, Feb 12 2021
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Mathematica
Select[Range[2, 600], Function[{d, k}, AnyTrue[d, Mod[#, k] != 0 &]] @@ {Divisors[#] - 1, FactorInteger[#][[1, 1]] - 1} &] (* Michael De Vlieger, Feb 12 2021 *)
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