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A143512 Numbers of the form 3^a 5^b 17^c 257^d 65537^e; products of Fermat primes. 7


%S 1,3,5,9,15,17,25,27,45,51,75,81,85,125,135,153,225,243,255,257,289,

%T 375,405,425,459,625,675,729,765,771,867,1125,1215,1275,1285,1377,

%U 1445,1875,2025,2125,2187,2295,2313,2601,3125,3375,3645,3825,3855,4131,4335,4369

%N Numbers of the form 3^a 5^b 17^c 257^d 65537^e; products of Fermat primes.

%C Similar to A004729, which allows each Fermat prime to occur 0 or 1 times. Applying Euler's phi function to these numbers produces numbers in A143513.

%C If the well known conjecture that, there are only five prime Fermat numbers F_k=2^{2^k}+1, k=0,1,2,3,4, is true, then exactly we have sum_{n=1,...,infty} 1/a(n) = prod_{k=0,...,4} F_k/(F_k-1) = 4294967295/2147483648 = 1.9999999995343387126922607421875. [Vladimir Shevelev and T. D. Noe, Dec 01 2010]

%H T. D. Noe, <a href="/A143512/b143512.txt">Table of n, a(n) for n=1..10000</a>

%t nn=60; logs=Log[2.,{3,5,17,257,65537}]; lim=Floor[nn/logs]; t={}; Do[z={i,j,k,l,m}.logs; If[z<nn, AppendTo[t,Round[2.^z]]], {i,0,lim[[1]]}, {j,0,lim[[2]]}, {k,0,lim[[3]]}, {l,0,lim[[4]]}, {m,0,lim[[5]]}]; t=Sort[t]

%K nonn

%O 1,2

%A _T. D. Noe_, Aug 21 2008

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Last modified December 5 20:39 EST 2021. Contains 349558 sequences. (Running on oeis4.)