A084227 Numbers of the form p*q^k with distinct primes p and q, k>0.

6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 68, 69, 74, 75, 76, 77, 80, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 104, 106, 111, 112, 115, 116, 117, 118, 119, 122, 123, 124, 129

Offset

1,1

Comments

A001221(a(n)) = 2 AND A001222(a(n)) = A051903(a(n)) + 1. [Clarified by N. J. A. Sloane, Aug 22 2021]

See A007774 for the numbers with omega(n) = A001221(n) = 2. - N. J. A. Sloane, Aug 22 2021

Links

Georg Fischer, Table of n, a(n) for n = 1..1000 [First 74 terms from G. C. Greubel]

Formula

a(n) ~ n log n/log log n. - Charles R Greathouse IV, Oct 19 2015

Example

80 = 5*2^4, therefore 80 is a term.
146 = 2*73, therefore 146 is a term.

Mathematica

Select[Range[160], (fal = Last/@FactorInteger[#]; And[Length[fal] == 2 && Min[fal] == 1]) &] (* Georg Fischer, Mar 01 2026 *)

Prog

(PARI) is(n)=my(f=factor(n)[, 2]); #f==2 && vecmin(f)==1 \\ Charles R Greathouse IV, Oct 19 2015

Crossrefs

Cf. A000961, A006881, A007774.

Sequence in context: A275665 A056760 A328956 * A299992 A237051 A390289

Adjacent sequences: A084224 A084225 A084226 * A084228 A084229 A084230

Keyword

nonn

Author

Reinhard Zumkeller, May 20 2003

Status

approved