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A143958 Integers n > 1 such that n-1 is divisible by the difference between the largest and smallest primes dividing n.

%I A143958 #14 Nov 27 2017 22:55:34
%S A143958 6,10,12,15,18,21,24,33,35,36,40,45,48,54,55,56,65,72,75,77,78,85,91,
%T A143958 96,100,105,108,126,133,135,136,143,144,145,154,160,161,162,175,187,
%U A143958 189,192,196,209,216,217,221,225,245,247,250,253,261,288,297,323,324,336
%N A143958 Integers n > 1 such that n-1 is divisible by the difference between the largest and smallest primes dividing n.
%C A143958 If p is prime, (p+t)*p is in the sequence if t is a divisor of p^2-1 such that p+t is prime. - _Robert Israel_, Nov 27 2017
%H A143958 Robert Israel, <a href="/A143958/b143958.txt">Table of n, a(n) for n = 1..10000</a>
%e A143958 The largest prime dividing 21 is 7. The smallest prime dividing 21 is 3. 7-3 = 4 divides 21-1 = 20. So 21 is in the sequence.
%p A143958 filter:= proc(n) local F;
%p A143958   F:= [min,max](numtheory:-factorset(n));
%p A143958   F[1]<F[2] and (n-1 mod (F[2]-F[1]) = 0)
%p A143958 end proc:
%p A143958 select(filter, [$2..1000]); # _Robert Israel_, Nov 27 2017
%t A143958 Select[Range[2, 336], Function[n, If[# == 0, False, Divisible[n - 1, #]] &[Last@ # - First@ #] &[FactorInteger[n][[All, 1]] ] ] ] (* _Michael De Vlieger_, Nov 27 2017 *)
%Y A143958 Cf. A143957.
%K A143958 nonn
%O A143958 1,1
%A A143958 _Leroy Quet_, Sep 05 2008
%E A143958 Extended by _Ray Chandler_, Nov 07 2008
%E A143958 Name edited by _Jon E. Schoenfield_, Nov 27 2017