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A143513 Numbers of the form 2^a 3^b 5^c 17^d 257^e 65537^f; products of 2 and the Fermat primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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,...,infty} 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

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Last modified October 17 13:29 EDT 2021. Contains 348049 sequences. (Running on oeis4.)