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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A358666 A349064 A124144 * A061040 A159456 A316483

Adjacent sequences: A276561 A276562 A276563 * A276565 A276566 A276567

Keyword

nonn

Author

Antonio Roldán, Nov 16 2016

Status

approved