cp's OEIS Frontend

A340449 Nonsquare composites n whose smallest prime factor is greater than or equal to n^(2/5).

%I A340449 #28 May 31 2024 22:05:21
%S A340449 15,35,55,77,91,119,143,187,209,221,247,253,299,319,323,341,377,391,
%T A340449 403,437,481,493,527,533,551,559,589,629,667,697,703,713,731,779,799,
%U A340449 817,851,893,899,901,943,989,1003,1007,1037,1073,1081,1121,1139,1147,1159,1189
%N A340449 Nonsquare composites n whose smallest prime factor is greater than or equal to n^(2/5).
%C A340449 Referred to as "freak-show composites" by Doug Massey (see link), who noted that they are exceptionally difficult to factor by hand using trial division.
%C A340449 4181, 4183, 4187, and 4189 are the first four consecutive terms that differ only in the last decimal digit.  The next such set of four consecutive terms begins at 806621.
%C A340449 Ankit Bisain says that for sufficiently large x, there are fewer values in this sequence less than x than there are primes less than x.
%H A340449 Quora, <a href="https://www.quora.com/What-s-the-definition-of-a-freak-show-composite-number/answer/Doug-Massey">What's the definition of a freak-show composite number?</a>
%e A340449 The smallest prime factor of 4189 is 59, which is greater than 4189^(2/5).
%p A340449 q:= n-> not (isprime(n) or issqr(n) or min(numtheory[factorset](n))^5<n^2):
%p A340449 select(q, [$4..2030])[];  # _Alois P. Heinz_, Jan 07 2021
%t A340449 nscQ[n_]:=CompositeQ[n]&&!IntegerQ[Sqrt[n]]&&FactorInteger[n][[1,1]]>= Surd[n^2,5]; Select[Range[1200],nscQ] (* _Harvey P. Dale_, Jul 25 2021 *)
%o A340449 (PARI) isok(n) = (n>1) && !isprime(n) && !issquare(n) && (factor(n)[1,1]^5 >= n^2); \\ _Michel Marcus_, Jan 07 2021
%Y A340449 Superset of A006094, except for initial 6 in that sequence.
%Y A340449 Subsequence of A089229.
%K A340449 nonn
%O A340449 1,1
%A A340449 _Phil Scovis_, Jan 07 2021