cp's OEIS Frontend

A340268 Composite numbers k>1 such that (s-1) | (d-1) for each d | k, where s = lpf(k) = A020639(k).

%I A340268 #43 Feb 16 2021 13:33:41
%S A340268 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,36,38,
%T A340268 39,40,42,44,45,46,48,49,50,51,52,54,56,57,58,60,62,63,64,65,66,68,69,
%U A340268 70,72,74,75,76,78,80,81,82,84,85,86,87,88,90,91,92,93,94,96
%N A340268 Composite numbers k>1 such that (s-1) | (d-1) for each d | k, where s = lpf(k) = A020639(k).
%C A340268 Not a duplicate of A340058 because the complements A335902 and A340269 differ. - _R. J. Mathar_, Feb 16 2021
%p A340268 with(numtheory):
%p A340268 q:= n-> (f-> andmap(d-> irem(d-1, f)=0, divisors(n)))(min(factorset(n))-1):
%p A340268 select(not isprime and q, [$2..96])[];  # _Alois P. Heinz_, Feb 12 2021
%t A340268 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 *)
%o A340268 (MATLAB)
%o A340268 n=300; % gives all terms of the sequence not exceeding n
%o A340268 A=[];
%o A340268 for i=2:n
%o A340268     lpf=2;
%o A340268     while mod(i,lpf)~=0
%o A340268         lpf=lpf+1;
%o A340268     end
%o A340268     for d=1:floor(i/2)
%o A340268         if mod(i,d)==0 && mod(d-1,lpf-1)~=0
%o A340268             break
%o A340268         elseif d==floor(i/2)
%o A340268             A=[A i];
%o A340268         end
%o A340268     end
%o A340268 end
%o A340268 (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
%Y A340268 Cf. A000010, A000961, A020639, A340058, A335902, A340269 (complement).
%Y A340268 Contains all composite terms of at least A003586, A003591, A003592, A003593, A003596.
%K A340268 nonn
%O A340268 1,1
%A A340268 _Maxim Karimov_, Jan 02 2021