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Numbers that are the sum of two proper prime powers (A246547).
1

%I #18 Jul 22 2017 10:19:09

%S 8,12,13,16,17,18,20,24,25,29,31,32,33,34,35,36,40,41,43,48,50,52,53,

%T 54,57,58,59,64,65,68,72,73,74,76,80,81,85,89,90,91,96,97,98,106,108,

%U 113,125,128,129,130,132,133,134,136,137,141,144,145,146,148,150,152,153,155,157,160,162,170,173,174,177,178

%N Numbers that are the sum of two proper prime powers (A246547).

%C Is 2213 the largest prime term that can be expressed as the sum of two proper prime powers in more than one way? - _Altug Alkan_, Jul 22 2017

%H Robert Israel, <a href="/A290135/b290135.txt">Table of n, a(n) for n = 1..10000</a>

%F Exponents in expansion of (Sum_{k>=1} x^A246547(k))^2.

%e 13 is in the sequence because 13 = 2^2 + 3^2.

%p N:= 1000: # to get all terms <= N

%p P:= select(isprime, [$2..floor(sqrt(N))]):

%p PP:= {seq(seq(p^j, j=2..floor(log[p](N))),p=P)}:

%p A:= select(`<=`,{seq(seq(PP[i]+PP[j],j=1..i),i=1..nops(PP))},N):

%p sort(convert(A,list)); # _Robert Israel_, Jul 21 2017

%t nmax = 180; f[x_] := Sum[Boole[PrimePowerQ[k] && PrimeOmega[k] > 1] x^k, {k, 1, nmax}]^2; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]

%Y Cf. A014091, A070049, A071330, A071331, A225102, A225103, A246547.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Jul 20 2017