

A276564


Perfect powers n (exponent greater than 1) such that n1 and n+1 are both semiprime.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..34.


EXAMPLE

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


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(i1)==2&&bigomega(i+1)==2, print1(i, ", ")))


CROSSREFS

Cf. A001597, A108278, A121898, A124936, A167023, A268043, A276565.
Sequence in context: A135780 A069701 A124144 * A061040 A159456 A316483
Adjacent sequences: A276561 A276562 A276563 * A276565 A276566 A276567


KEYWORD

nonn


AUTHOR

Antonio Roldán, Nov 16 2016


STATUS

approved



