OFFSET
1,2
COMMENTS
a(n) is the product of n, floor(log_2 n), floor (log_2(log_2 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
EXAMPLE
a(0) is the product of 0 numbers, defined to be 1.
a(15) = 15 * floor(log_2 15) * floor(log_2 log_2 15) = 15 * 3 * 1 = 45.
a(17) = 17 * floor(log_2 17) * floor(log_2 log_2 17) * floor(log_2 log_2 log_2 17) = 17 * 4 * 2 * 1 = 136.
MATHEMATICA
Table[prod = 1; s = n; While[s > 1, prod = prod*Floor[s]; s = Log[2, s]]; prod, {n, 60}] (* T. D. Noe, Sep 24 2012 *)
PROG
(Haskell) a = product . map floor . takeWhile (1<) . iterate log_2
(PARI) a(n)=my(t=n); n+=1e-9; while(n>2, t*=floor(n=log(n)/log(2))); t \\ Charles R Greathouse IV, Sep 25 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Ken Takusagawa, Sep 15 2012
STATUS
approved