A080364 Composite numbers whose least prime factor appears with multiplicity 1.

6, 10, 14, 15, 18, 21, 22, 26, 30, 33, 34, 35, 38, 39, 42, 46, 50, 51, 54, 55, 57, 58, 62, 65, 66, 69, 70, 74, 75, 77, 78, 82, 85, 86, 87, 90, 91, 93, 94, 95, 98, 102, 105, 106, 110, 111, 114, 115, 118, 119, 122, 123, 126, 129, 130, 133, 134, 138, 141, 142, 143, 145, 146

Offset: 1

Author

Labos Elemer, Feb 21 2003

Keywords

• nonn
• easy

Comments

Density is Sum_{p >= 2} 1/p * Product_{q <= p} (1 - 1/q) which is around 0.65. (In the sum and product, p and q are restricted to primes.) - Charles R Greathouse IV, Jan 09 2022

Examples

			50 = 2^1 * 5^2; least prime factor is 2, whose exponent is 1, so 50 is a term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034444, A056169, A020639, A080363.

Programs

Mathematica

mi[x_] := Part[Flatten[FactorInteger[x]], 1] k=0; Do[s=mi[n]; If[Equal[GCD[s, n/s], 1]&&!PrimeQ[n], Print[n]], {n, 2, 256}]
Select[Range[150],CompositeQ[#]&&FactorInteger[#][[1,2]]==1&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 23 2021 *)

PARI

is(n,f=factor(n))=n>1 && f[1,2]==1 \\ Charles R Greathouse IV, Jan 09 2022

PARI

is(n)=forprime(p=2,97, if(n%p==0, return(n%p^2>0))); !ispower(n) && factor(n)[1,2]==1 \\ Charles R Greathouse IV, Jan 09 2022

Extensions

Edited by Jon E. Schoenfield, Jul 10 2018