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A189045 Semiprimes which are sub-perfect powers. 3
15, 26, 35, 143, 215, 323, 511, 899, 1727, 1763, 2047, 2186, 2743, 3599, 5183, 7999, 10403, 11663, 13823, 19043, 22499, 32399, 36863, 39203, 51983, 54871, 57599, 72899, 79523, 97343, 121103, 157463, 176399, 186623, 213443, 238327, 248831, 272483, 279935, 324899, 359999, 381923 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers of the form p*q where p and q are primes, not necessarily distinct, such that p*q + 1 is a perfect power (squares, cubes, etcetera). In one sense, this is to semiprimes as Mersenne primes A000668 are to primes.

By Catalan's conjecture (or now Mihailescu's theorem), p and q are always distinct. - T. D. Noe, Apr 15 2011

LINKS

T. D. Noe, Table of n, a(n) for n = 1..8433 (terms < 10^12)

FORMULA

A001358 INTERSECTION A045542. A001358 INTERSECTION {A001597 - 1}.

EXAMPLE

a(9) = (12^3)-1 = 1727 = 11 * 157.

MATHEMATICA

SemiPrimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; PerfectPowerQ[n_] := GCD @@ Last /@ FactorInteger[n] > 1; Select[Range[400000], SemiPrimeQ[#] && PerfectPowerQ[# + 1] &] (* T. D. Noe, Apr 15 2011 *)

CROSSREFS

Cf. A001358, A001597, A045542, A177955, A189047.

Sequence in context: A074974 A191913 A191915 * A032609 A050699 A097393

Adjacent sequences:  A189042 A189043 A189044 * A189046 A189047 A189048

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Apr 15 2011

STATUS

approved

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Last modified October 14 17:31 EDT 2019. Contains 328022 sequences. (Running on oeis4.)