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Numbers with largest and smallest prime factors differing by 6.
4

%I #11 May 14 2024 04:33:02

%S 55,91,187,247,275,385,391,605,637,667,1001,1147,1183,1375,1591,1925,

%T 1927,2057,2431,2491,2695,3025,3127,3179,3211,4087,4199,4235,4459,

%U 4693,4891,5767,6647,6655,6875,7007,7387,7429,8281,8993,9625,9991,10807,11011

%N Numbers with largest and smallest prime factors differing by 6.

%H Reinhard Zumkeller, <a href="/A195118/b195118.txt">Table of n, a(n) for n = 1..250</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SexyPrimes.html">Sexy Primes</a>. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- _N. J. A. Sloane_, Mar 07 2021]

%e a(10) = 667 = 23 * 29;

%e a(11) = 1001 = 7 * 11 * 13;

%e a(12) = 1147 = 31 * 37;

%e a(13) = 1183 = 7 * 13^2.

%t spf6Q[n_]:=With[{fi=FactorInteger[n]},fi[[-1,1]]-fi[[1,1]]==6]; Select[Range[12000],spf6Q] (* _Harvey P. Dale_, May 14 2024 *)

%o (Haskell)

%o a195118 n = a195118_list !! (n-1)

%o a195118_list = filter f [3,5..] where

%o f x = last pfs - head pfs == 6 where pfs = a027748_row x

%Y Cf. A195106, A111192; A143205 is a subsequence.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Sep 13 2011