A340269 - OEIS

%I #52 Oct 11 2023 08:42:46

%S 35,55,77,95,115,119,143,155,161,175,187,203,209,215,221,235,245,247,

%T 253,275,287,295,299,319,323,329,335,355,371,377,385,391,395,403,407,

%U 413,415,437,455,473,475,493,497,515,517,527,533,535,539,551,559,575,581

%N 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 No terms are divisible by 2 or 3; no terms are in A000961. - _Robert Israel_, Oct 10 2023

%H Robert Israel, <a href="/A340269/b340269.txt">Table of n, a(n) for n = 1..10000</a>

%p with(numtheory):

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

%p select(q, [$2..600])[];  # _Alois P. Heinz_, Feb 12 2021

%t 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 (MATLAB)

%o n=300; % gives all terms of the sequence not exceeding n

%o A=[];

%o for i=2:n

%o     lpf=2;

%o     while mod(i,lpf)~=0

%o         lpf=lpf+1;

%o     end

%o     for d=1:i

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

%o             A=[A i];

%o             break

%o         end

%o     end

%o end

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

%K nonn

%O 1,1

%A _Maxim Karimov_, Jan 02 2021