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

15, 35, 55, 77, 91, 119, 143, 187, 209, 221, 247, 253, 299, 319, 323, 341, 377, 391, 403, 437, 481, 493, 527, 533, 551, 559, 589, 629, 667, 697, 703, 713, 731, 779, 799, 817, 851, 893, 899, 901, 943, 989, 1003, 1007, 1037, 1073, 1081, 1121, 1139, 1147, 1159, 1189

Offset: 1

Author

Phil Scovis, Jan 07 2021

Keywords

• nonn

Comments

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.

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.

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.

Examples

			The smallest prime factor of 4189 is 59, which is greater than 4189^(2/5).
		

Links

• Quora, What's the definition of a freak-show composite number?

Crossrefs

Superset of A006094, except for initial 6 in that sequence.

Subsequence of A089229.

Programs

Maple

q:= n-> not (isprime(n) or issqr(n) or min(numtheory[factorset](n))^5Alois P. Heinz, Jan 07 2021

Mathematica

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 *)

PARI

isok(n) = (n>1) && !isprime(n) && !issquare(n) && (factor(n)[1,1]^5 >= n^2); \\ Michel Marcus, Jan 07 2021