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

1, 3, 5, 9, 15, 17, 25, 27, 45, 51, 75, 81, 85, 125, 135, 153, 225, 243, 255, 257, 289, 375, 405, 425, 459, 625, 675, 729, 765, 771, 867, 1125, 1215, 1275, 1285, 1377, 1445, 1875, 2025, 2125, 2187, 2295, 2313, 2601, 3125, 3375, 3645, 3825, 3855, 4131, 4335, 4369

Offset: 1

Author

T. D. Noe, Aug 21 2008

Keywords

• nonn

Comments

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.

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 we have exactly Sum_{n>=1} 1/a(n) = Product_{k=0..4} F_k/(F_k-1) = 4294967295/2147483648 = 1.9999999995343387126922607421875. - Vladimir Shevelev and T. D. Noe, Dec 01 2010

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Programs

Mathematica

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