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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..53.

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: A043915 A318572 A171082 * A335902 A121707 A267999

Adjacent sequences:  A340266 A340267 A340268 * A340270 A340271 A340272

KEYWORD

nonn

AUTHOR

Maxim Karimov, Jan 02 2021

STATUS

approved

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Last modified April 16 18:21 EDT 2021. Contains 343050 sequences. (Running on oeis4.)