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A216762 n * log(n) * log(log(n)) * log(log(log(n))) ... with base-2 logarithms and ceiling applied to each factor. 1
1, 2, 6, 8, 30, 36, 42, 48, 72, 80, 88, 96, 104, 112, 120, 128, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 870, 900, 930, 960, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728, 1764, 1800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the product of n, ceil(log2 n), ceil(log2(log2 n)),... with the base-2 logs iterated while the result remains greater than unity.

The sum of the reciprocals of a(n) diverge, but extremely slowly.

In particular, the sum of the reciprocals acts like lg* n asymptotically, where lg* x = 0 for x < 2 and lg* 2^x = 1 + lg* x. - Charles R Greathouse IV, Sep 25 2012

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

a(0) is the product of 0 numbers, defined to be 1.

a(15) = 15 * ceil(log2 15) * ceil(log2 log2 15) * ceil(log2 log2 log2 15) = 15 * 4 * 2 * 1 = 120.

a(17) = 17 * ceil(log2 17) * ceil(log2 log2 17) * ceil(log2 log2 log2 17) * ceil(log2 log2 log2 log2 17) = 17 * 5 * 3 * 2 * 1 = 510.

MATHEMATICA

Table[prod = 1; s = n; While[s > 1, prod = prod*Ceiling[s]; s = Log[2, s]]; prod, {n, 50}] (* T. D. Noe, Sep 24 2012 *)

PROG

(Haskell) a = product . map ceil . takeWhile (1<) . iterate log_2

(PARI) a(n)=my(t=n); n-=1e-9; while(n>2, t*=ceil(n=log(n)/log(2))); t \\ Charles R Greathouse IV, Sep 25 2012

CROSSREFS

Cf. A216761 (floor instead of ceiling).

Sequence in context: A020696 A290249 A321471 * A132269 A053287 A086323

Adjacent sequences:  A216759 A216760 A216761 * A216763 A216764 A216765

KEYWORD

nonn

AUTHOR

Ken Takusagawa, Sep 15 2012

STATUS

approved

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Last modified May 26 15:29 EDT 2019. Contains 323597 sequences. (Running on oeis4.)