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A143512 Numbers of the form 3^a 5^b 17^c 257^d 65537^e; products of Fermat primes. 7
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 (list; graph; refs; listen; history; text; internal format)
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 exactly we have sum_{n=1,...,infty} 1/a(n) = prod_{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

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Last modified October 26 06:08 EDT 2021. Contains 348257 sequences. (Running on oeis4.)