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A340268 Composite numbers k>1 such that (s-1) | (d-1) for each d | k, where s = lpf(k) = A020639(k). 1
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Not a duplicate of A340058 because the complements A335902 and A340269 differ. - R. J. Mathar, Feb 16 2021

LINKS

Table of n, a(n) for n=1..67.

MAPLE

with(numtheory):

q:= n-> (f-> andmap(d-> irem(d-1, f)=0, divisors(n)))(min(factorset(n))-1):

select(not isprime and q, [$2..96])[];  # Alois P. Heinz, Feb 12 2021

MATHEMATICA

Select[Range[2, 96], Function[{n, s}, And[! PrimeQ@ n, AllTrue[Divisors[n] - 1, Mod[#, s] == 0 &]]] @@ {#, 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:floor(i/2)

        if mod(i, d)==0 && mod(d-1, lpf-1)~=0

            break

        elseif d==floor(i/2)

            A=[A i];

        end

    end

end

(PARI) isok(c) = if ((c>1) && !isprime(c), my(f=factor(c)[, 1]); for (k=1, #f~, if ((f[k]-1) % (f[1]-1), return(0))); return(1)); \\ Michel Marcus, Jan 03 2021

CROSSREFS

Cf. A000010, A000961, A020639, A340058, A335902, A340269 (complement).

Contains all composite terms of at least A003586, A003591, A003592, A003593, A003596.

Sequence in context: A140347 A140209 A077091 * A340058 A174891 A051035

Adjacent sequences:  A340265 A340266 A340267 * A340269 A340270 A340271

KEYWORD

nonn

AUTHOR

Maxim Karimov, Jan 02 2021

STATUS

approved

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Last modified October 20 08:28 EDT 2021. Contains 348099 sequences. (Running on oeis4.)