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

%I

%S 144,216,900,1764,2048,3600,10404,11664,39204,97344,213444,248832,

%T 272484,360000,656100,685584,1040400,1102500,1127844,1633284,2108304,

%U 2214144,3504384,3802500,4112784,4536900,4588164,5475600,7784100,7851204,8388608,8820900,9000000,9734400

%N Perfect powers n (exponent greater than 1) such that n-1 and n+1 are both semiprime.

%C Intersection of A001597 and A124936. - _Michel Marcus_, Dec 03 2016

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

%t 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 *)

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

%Y Cf. A001597, A108278, A121898, A124936, A167023, A268043, A276565.

%K nonn

%O 1,1

%A _Antonio Roldán_, Nov 16 2016

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)