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

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, 50, 51, 54, 60, 64, 68, 72, 75, 80, 81, 85, 90, 96, 100, 102, 108, 120, 125, 128, 135, 136, 144, 150, 153, 160, 162, 170, 180, 192, 200, 204, 216, 225, 240, 243, 250, 255, 256

Offset: 1

Author

T. D. Noe, Aug 21 2008

Keywords

• nonn

Comments

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.

Links

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

Programs

Mathematica

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
				

Formula

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} 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