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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A034444, A056169, A020639, A080363.

Sequence in context: A069169 A230766 A231877 * A325230 A227299 A082092

Adjacent sequences: A080361 A080362 A080363 * A080365 A080366 A080367

Keyword

nonn,easy

Author

Labos Elemer, Feb 21 2003

Extensions

Edited by Jon E. Schoenfield, Jul 10 2018

Status

approved