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A282550 Perfect powers that are the sum of two distinct proper prime powers (A246547). 4
25, 36, 81, 125, 144, 196, 324, 512, 576, 1089, 2304, 2744, 2916, 5041, 9216, 14884, 16641, 26244, 36864, 51984, 147456, 236196, 589824, 941192, 1196836, 2125764, 2359296, 9437184, 19131876, 37748736, 67125249, 150994944, 172186884, 322828856, 603979776 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A001597 and A225102. - Michel Marcus, Feb 18 2017

Terms t of A001597 such that A225099(t) > 0. - Felix Fröhlich, Feb 18 2017

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..45 (terms < 2*10^11)

EXAMPLE

512 = 2^9 is a term because 2^9 = 7^3 + 13^2.

MATHEMATICA

Select[Union@ Map[Total, Subsets[With[{nn = 10^6}, Complement[ Select[ Range@ nn, PrimePowerQ], Prime[Range[PrimePi@ nn]]]], {2}]], # == 1 ||

GCD @@ FactorInteger[#][[All, 2]] > 1 &] (* Michael De Vlieger, Feb 18 2017, after Harvey P. Dale at A246547 *)

PROG

(PARI) is(n) = if(!ispower(n), return(0), my(x=n-1, y=1); while(y < x, if(isprimepower(x) && isprimepower(y) && !ispseudoprime(x) && !ispseudoprime(y), return(1)); y++; x--)); 0 \\ Felix Fröhlich, Feb 18 2017

CROSSREFS

Cf. A001597, A225099, A225102, A225106, A246547.

Sequence in context: A263095 A077502 A297415 * A265505 A162305 A029773

Adjacent sequences:  A282547 A282548 A282549 * A282551 A282552 A282553

KEYWORD

nonn

AUTHOR

Altug Alkan, Feb 18 2017

EXTENSIONS

More terms from Felix Fröhlich, Feb 18 2017

a(28)-a(35) from Giovanni Resta, May 07 2017

STATUS

approved

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Last modified February 25 20:52 EST 2020. Contains 332258 sequences. (Running on oeis4.)