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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..250

Eric Weisstein's World of Mathematics, Cousin Primes.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A023200, A143206, A195118.

A143203 is a subsequence.

Sequence in context: A219856 A371112 A371052 * A143203 A082060 A025525

Adjacent sequences: A195103 A195104 A195105 * A195107 A195108 A195109

Keyword

nonn

Author

Reinhard Zumkeller, Sep 13 2011

Status

approved