|
Search: id:A077643
|
|
|
| A077643 |
|
Number of square-free integers in closed interval [2^n,-1+2*2^n], i.e. among 2^n consecutive numbers beginning with 2^n. |
|
+0
2
|
|
| 1, 2, 3, 5, 9, 19, 39, 79, 157, 310, 621, 1246, 2491, 4980, 9958, 19924, 39844, 79672, 159365, 318736, 637457, 1274916, 2549816, 5099651, 10199363, 20398663, 40797299, 81594571, 163189087, 326378438, 652756861, 1305513511, 2611026987
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
FORMULA
|
a(n)=Sum[Abs(mu[2^n+j]); j=0...-1+2^n)]
a(n)/2^n approaches 1/Zeta[2], so limiting sequence is Table[Floor[2^n/Zeta[2]], {n, 0, 36}] - Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 25 2003
|
|
EXAMPLE
|
n=4: among 16 numbers of {16,...,31}, nine are square-free [17,19,21,22,23,26,29,30,31], so a(4)=9.
|
|
MATHEMATICA
|
Table[Apply[Plus, Table[Abs[MoebiusMu[2^w+j]], {j, 0, 2^w-1}]], {w, 0, 15}]
|
|
PROGRAM
|
(PARI) { a(n) = sum(m=1, sqrtint(2^(n+1)-1), moebius(m) * ((2^(n+1)-1)\m^2 - (2^n-1)\m^2) ) } [From Max Alekseyev (maxal(AT)cs.ucsd.edu), Oct 18 2008]
|
|
CROSSREFS
|
Cf. A077641, A077642.
Sequence in context: A003218 A058770 A049910 this_sequence A123389 A113984 A110542
Adjacent sequences: A077640 A077641 A077642 this_sequence A077644 A077645 A077646
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Labos E. (labos(AT)ana.sote.hu), Nov 14 2002
|
|
EXTENSIONS
|
More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 12 2003
More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 25 2003
a(25) and up from Max Alekseyev (maxal(AT)cs.ucsd.edu), Oct 18 2008
|
|
|
Search completed in 0.002 seconds
|
