A195106 Numbers with largest and smallest prime factors differing by 4.

21, 63, 77, 105, 147, 189, 221, 315, 437, 441, 525, 539, 567, 735, 847, 945, 1029, 1323, 1517, 1575, 1701, 2021, 2205, 2625, 2835, 2873, 3087, 3675, 3757, 3773, 3969, 4725, 4757, 5103, 5145, 5929, 6557, 6615, 7203, 7875, 8303, 8505, 9261, 9317, 9797, 10051

Offset: 1

Author

Reinhard Zumkeller, Sep 13 2011

Keywords

• nonn

Examples

			a(10) = 441 = 3^2 * 7^2.
a(11) = 525 = 3 * 5^2 * 7.
a(12) = 539 = 7^2 * 11.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..250
• Eric Weisstein's World of Mathematics, Cousin Primes.

Crossrefs

Cf. A023200, A143206, A195118.

A143203 is a subsequence.

Programs

Haskell

a195106 n = a195106_list !! (n-1)
a195106_list = filter (\x -> a006530 x - a020639 x == 4) [1,3..]

Mathematica

pf4Q[n_]:=Module[{pfs=Transpose[FactorInteger[n]][[1]]}, Max[pfs]- Min[pfs]==4]; Select[Range[11000],pf4Q] (* Harvey P. Dale, Sep 24 2011 *)

Formula

Sum_{n>=1} 1/a(n) = 1/48 + Sum_{n>=1} 1/A143203(n) = 1/48 + Sum_{n>=1} 1/((A023200(n)+1)^2-4) = 0.130715767205... . - Amiram Eldar, Oct 26 2024