A088072 Numbers sandwiched between two numbers having only one prime divisor (at least) one of which is composite.

3, 8, 10, 24, 26, 28, 48, 80, 82, 126, 168, 242, 360, 728, 840, 1368, 1848, 2208, 2400, 3720, 5040, 6562, 6858, 7920, 10608, 11448, 14640, 16128, 17160, 19320, 19682, 24390, 28560, 29790, 29928, 36480, 44520, 49728, 50652, 54288, 57120, 59050

Offset: 1

Author

Amarnath Murthy, Sep 22 2003

Keywords

• nonn

Comments

Terms of A088071 which are not terms of A014574 (average of twin prime pairs).

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).

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A088071, A014574.

Programs

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,",")))}

Extensions

Edited and extended by Klaus Brockhaus, Sep 25 2003