A195238 Numbers with at least 2 and not more than 3 distinct prime factors not greater than 7 that are multiples of 7 or of 15.

14, 15, 21, 28, 30, 35, 42, 45, 56, 60, 63, 70, 75, 84, 90, 98, 105, 112, 120, 126, 135, 140, 147, 150, 168, 175, 180, 189, 196, 224, 225, 240, 245, 252, 270, 280, 294, 300, 315, 336, 350, 360, 375, 378, 392, 405, 441, 448, 450, 480, 490, 504, 525, 540, 560

Offset: 1

Author

Harvey P. Dale, Sep 13 2011

Keywords

• nonn
• easy

Comments

A143204 is a subsequence.

Subsequence of A002473.

Examples

			a(10) = 60 = 2^2 * 3 * 5.
a(11) = 63 = 3^2 * 7.
a(12) = 70 = 2 * 5 * 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221, A006530, A143204, A002473.

Programs

Haskell

a195238 n = a195238_list !! (n-1)
a195238_list = filter (\x -> a001221 x `elem` [2,3] &&
                             a006530 x `elem` [5,7] &&
                             (mod x 7 == 0 || mod x 15 == 0)) [1..]
-- Reinhard Zumkeller, Sep 13 2011

Mathematica

pfsQ[n_]:=Module[{fs=Transpose[FactorInteger[n]][[1]]},Max[fs]<8 && 1Harvey P. Dale, Aug 21 2011 *)

PARI

is(n)=my(v=apply(p->valuation(n,p), [2,3,5,7])); n==2^v[1]*3^v[2]*5^v[3]*7^v[4] && (v[4] || v[2]*v[3]) && factorback(v)==0 && !!v[1]+!!v[2]+!!v[3]+!!v[4]>1 \\ Charles R Greathouse IV, Sep 14 2015

Formula

2 <= A001221(a(n)) <= 3.

5 <= A006530(a(n)) <= 7.

Sum_{n>=1} 1/a(n) = 11/16. - Amiram Eldar, Oct 25 2024