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

1,1

Comments

No terms are divisible by 2 or 3; no terms are in A000961. - Robert Israel, Oct 10 2023

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A000010, A000961, A020639, A335902, A340058, A340268.

Sequence in context: A355812 A318572 A171082 * A335902 A121707 A267999

Adjacent sequences: A340266 A340267 A340268 * A340270 A340271 A340272

Keyword

nonn

Author

Maxim Karimov, Jan 02 2021

Status

approved