A276564 Perfect powers k (exponent greater than 1) such that k-1 and k+1 are both semiprime.

144, 216, 900, 1764, 2048, 3600, 10404, 11664, 39204, 97344, 213444, 248832, 272484, 360000, 656100, 685584, 1040400, 1102500, 1127844, 1633284, 2108304, 2214144, 3504384, 3802500, 4112784, 4536900, 4588164, 5475600, 7784100, 7851204, 8388608, 8820900, 9000000, 9734400

Offset: 1

Author

Antonio Roldán, Nov 16 2016

Keywords

• nonn

Comments

Intersection of A001597 and A124936. - Michel Marcus, Dec 03 2016

Examples

			2048 = 2^11, and both 2047 = 23*89 and 2049 = 3*683 are semiprimes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A001597, A108278, A121898, A124936, A167023, A268043, A276565.

Programs

Mathematica

Select[Range[10^7], And[GCD @@ FactorInteger[#][[All, 2]] > 1, Union@ # == {2} &@ Map[PrimeOmega, {# - 1, # + 1}]] &] (* Michael De Vlieger, Dec 07 2016, after Ant King at A001597 *)

PARI

for(i=2,10^7,if(ispower(i)&&bigomega(i-1)==2&&bigomega(i+1)==2,print1(i,", ")))