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

1,2

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

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

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<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]

Crossrefs

Sequence in context: A051250 A143071 A305759 * A062849 A243355 A233461

Adjacent sequences: A143510 A143511 A143512 * A143514 A143515 A143516

Keyword

nonn

Author

T. D. Noe, Aug 21 2008

Status

approved