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A376929 Products of 5 distinct primes that are sandwiched between sphenic numbers.

%I A376929 #22 Jan 11 2025 16:25:47
%S A376929 50610,52206,63546,65190,71890,73830,77406,84930,89310,89870,90390,
%T A376929 92598,98210,116754,119210,120990,123410,125994,131054,132430,132870,
%U A376929 137410,140998,141702,144430,148190,150306,151810,159942,160854,162470,164406,165110,167314,170562,172938,174306,176946,185658
%N A376929 Products of 5 distinct primes that are sandwiched between sphenic numbers.
%C A376929 All terms are even.
%C A376929 Dickson's conjecture implies that there are infinitely many terms, e.g. there should be infinitely many k such that p = 241 + 104533*k, q = 229 + 99330*k, and r = 107 + 46410*k are all prime, and then 210*p is a term (with 210*p = 2*3*5*7*p, 210*p-1 = 13*17*q, and 210*p+1 = 11*43*r). - _Robert Israel_, Nov 12 2024
%H A376929 Robert Israel, <a href="/A376929/b376929.txt">Table of n, a(n) for n = 1..10000</a>
%e A376929 50610 is a term because 50610=2*3*5*7*241 is the product of five distinct primes and 50609=13*17*229, 50611=11*43*107 are sphenic numbers.
%e A376929 52206 is a term because 52206=2*3*7*11*113 is the product of five distinct primes and 52205=5*53*197, 52207=17*37*83 are sphenic numbers.
%p A376929 filter:= proc(n) local F;
%p A376929   F:= ifactors(n)[2];
%p A376929   if F[..,2] <> [1$5] then return false fi;
%p A376929   F:= ifactors(n-1)[2];
%p A376929   if F[..,2] <> [1$3] then return false fi;
%p A376929   F:= ifactors(n+1)[2];
%p A376929   F[..,2] = [1$3]
%p A376929 end proc:
%p A376929 select(filter, [seq(i,i=2..2*10^5,4)]); # _Robert Israel_, Nov 12 2024
%t A376929 SequencePosition[Map[#[[;; , 2]] &, FactorInteger[Range[200000]]], {{1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1}}][[;; , 1]] + 1 (* _Amiram Eldar_, Oct 11 2024 *)
%Y A376929 Intersection of A046387 and 2*A376734.
%Y A376929 Cf. A376380, A351382, A007304.
%K A376929 nonn
%O A376929 1,1
%A A376929 _Massimo Kofler_, Oct 11 2024