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

1,2

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

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<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]

Crossrefs

Sequence in context: A129771 A209837 A093688 * A174688 A339345 A111249

Adjacent sequences: A143509 A143510 A143511 * A143513 A143514 A143515

Keyword

nonn

Author

T. D. Noe, Aug 21 2008

Status

approved