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A143513 Numbers of the form 2^a 3^b 5^c 17^d 257^e 65537^f; products of 2 and the Fermat primes. 3


%S 1,2,3,4,5,6,8,9,10,12,15,16,17,18,20,24,25,27,30,32,34,36,40,45,48,

%T 50,51,54,60,64,68,72,75,80,81,85,90,96,100,102,108,120,125,128,135,

%U 136,144,150,153,160,162,170,180,192,200,204,216,225,240,243,250,255,256

%N Numbers of the form 2^a 3^b 5^c 17^d 257^e 65537^f; products of 2 and the Fermat primes.

%C Similar to A003401, which allows each Fermat prime to occur 0 or 1 times. Euler's phi function maps this sequence into itself. The odd terms of this sequence are in A143512.

%H T. D. Noe, <a href="/A143513/b143513.txt">Table of n, a(n) for n=1..10000</a>

%F sum_{a(n)is odd} 1/a(n) = sum_{a(n)is even} 1/a(n). If there are only five Fermat primes: 3,5,17,257,65537 (this is a well known conjecture), then we have exactly sum_{n=1,...,infty} 1/a(n) = 4294967295/1073741824 = 3.999999999068677425384521484375, which is twice the sum of the reciprocals of A143512. [Vladimir Shevelev and T. D. Noe, Dec 01 2010]

%t nn=34; logs=Log[2.,{2,3,5,17,257,65537}]; lim=Floor[nn/logs]; t={}; Do[z={i,j,k,l,m,n}.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]]}, {n,0,lim[[6]]}]; t=Sort[t]

%K nonn

%O 1,2

%A _T. D. Noe_, Aug 21 2008

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Last modified November 27 20:49 EST 2021. Contains 349395 sequences. (Running on oeis4.)