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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).

%I A340269 #52 Oct 11 2023 08:42:46
%S A340269 35,55,77,95,115,119,143,155,161,175,187,203,209,215,221,235,245,247,
%T A340269 253,275,287,295,299,319,323,329,335,355,371,377,385,391,395,403,407,
%U A340269 413,415,437,455,473,475,493,497,515,517,527,533,535,539,551,559,575,581
%N 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).
%C A340269 No terms are divisible by 2 or 3; no terms are in A000961. - _Robert Israel_, Oct 10 2023
%H A340269 Robert Israel, <a href="/A340269/b340269.txt">Table of n, a(n) for n = 1..10000</a>
%p A340269 with(numtheory):
%p A340269 q:= n-> (f-> ormap(d-> irem(d-1, f)>0, divisors(n)))(min(factorset(n))-1):
%p A340269 select(q, [$2..600])[];  # _Alois P. Heinz_, Feb 12 2021
%t A340269 Select[Range[2, 600], Function[{d, k}, AnyTrue[d, Mod[#, k] != 0 &]] @@ {Divisors[#] - 1, FactorInteger[#][[1, 1]] - 1} &] (* _Michael De Vlieger_, Feb 12 2021 *)
%o A340269 (MATLAB)
%o A340269 n=300; % gives all terms of the sequence not exceeding n
%o A340269 A=[];
%o A340269 for i=2:n
%o A340269     lpf=2;
%o A340269     while mod(i,lpf)~=0
%o A340269         lpf=lpf+1;
%o A340269     end
%o A340269     for d=1:i
%o A340269         if mod(i,d)==0 && mod(d-1,lpf-1)~=0
%o A340269             A=[A i];
%o A340269             break
%o A340269         end
%o A340269     end
%o A340269 end
%Y A340269 Cf. A000010, A000961, A020639, A335902, A340058, A340268.
%K A340269 nonn
%O A340269 1,1
%A A340269 _Maxim Karimov_, Jan 02 2021