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%I #19 Dec 07 2019 00:47:23
%S 1,2,6,8,30,36,42,48,72,80,88,96,104,112,120,128,510,540,570,600,630,
%T 660,690,720,750,780,810,840,870,900,930,960,1188,1224,1260,1296,1332,
%U 1368,1404,1440,1476,1512,1548,1584,1620,1656,1692,1728,1764,1800
%N a(n) = n * ceiling(log_2(n)) * ceiling(log_2(log_2(n))) * ceiling(log_2(log_2(log_2(n)))) ....
%C a(n) is the product of n, ceiling(log_2(n)), ceiling(log_2(log_2(n))), ... with the base-2 logs iterated while the result remains greater than unity.
%C The sum of the reciprocals of a(n) diverge, but extremely slowly.
%C 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
%e a(0) is the product of 0 numbers, defined to be 1.
%e a(15) = 15 * ceiling(log_2(15)) * ceiling(log_2(log_2(15))) * ceiling(log_2(log_2(log_2(15)))) = 15 * 4 * 2 * 1 = 120.
%e a(17) = 17 * ceiling(log_2(17)) * ceiling(log_2(log_2(17))) * ceiling(log_2(log_2(log_2(17)))) * ceiling(log_2(log_2(log_2(log_2(17))))) = 17 * 5 * 3 * 2 * 1 = 510.
%t 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 *)
%o (Haskell) a = product . map ceil . takeWhile (1<) . iterate log_2
%o (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
%Y Cf. A216761 (floor instead of ceiling).
%K nonn
%O 1,2
%A _Ken Takusagawa_, Sep 15 2012
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