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%I #7 Sep 29 2019 02:50:54
%S 3,8,10,24,26,28,48,80,82,126,168,242,360,728,840,1368,1848,2208,2400,
%T 3720,5040,6562,6858,7920,10608,11448,14640,16128,17160,19320,19682,
%U 24390,28560,29790,29928,36480,44520,49728,50652,54288,57120,59050
%N Numbers sandwiched between two numbers having only one prime divisor (at least) one of which is composite.
%C Terms of A088071 which are not terms of A014574 (average of twin prime pairs).
%C Conjecture (1): Sequence is infinite. Conjecture (2): There are only finitely many terms which are sandwiched between composite numbers (26 is the only such term below 1000000).
%H Amiram Eldar, <a href="/A088072/b088072.txt">Table of n, a(n) for n = 1..1000</a>
%e 8 is a term since 7 is prime and 9 = 3*3 is composite; 26 is a term since 25 = 5*5 and 27 = 3*3*3 are both composite.
%o (PARI) {for(n=2,60000,if(matsize(factor(n-1))[1]*matsize(factor(n+1))[1]==1&&factor(n-1)[1,2]*factor(n+1)[1,2]>1,print1(n,",")))}
%Y Cf. A088071, A014574.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Sep 22 2003
%E Edited and extended by _Klaus Brockhaus_, Sep 25 2003