A088072 - OEIS

%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