|
|
A370093
|
|
Decimal expansion of Lichtman constant f(N*(2)).
|
|
6
|
|
|
8, 9, 0, 9, 2, 5, 4, 7, 9, 4, 7, 6, 3, 1, 8, 3, 3, 2, 1, 3, 7, 2, 6, 2, 6, 2, 1, 9, 9, 5, 9, 8, 8, 2, 9, 3, 8, 9, 7, 8, 1, 8, 1, 3, 8, 1, 6, 5, 2, 7, 6, 3, 8, 9, 8, 3, 2, 9, 0, 7, 5, 6, 6, 9, 9, 8, 9, 1, 3, 4, 4, 1, 0, 6, 1, 4, 5, 0, 5, 2, 0, 7, 3, 6, 6, 4, 9, 7, 3, 3, 5, 9, 2, 7, 6, 2, 3, 2, 7, 5, 0, 3, 3, 3, 8, 3
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Definition:
f(N*(k)) = Integral_{s>=1} P_k*(s), where P_k*(s) = Sum_{n>1 and (big) Omega(n)=k} mu(n)^2/n^s, where mu is Möbius (or Moebius) Mu function see A008683, and (big) Omega is number of prime divisors of n counted with multiplicity see A001222.
Lichtman constant f(N*(1)) see A137245.
Lichtman constant f(N*(2)) this sequence.
Lichtman constant f(N*(3)) see A370112.
Lichtman constant f(N*(4)) see A370113.
when k -> oo than f(N*(k) -> 6/Pi^2 = 0.607927101854... see A059956.
Value computed and communicated by Bill Allombert.
|
|
LINKS
|
|
|
EXAMPLE
|
0.890925479476318332...
|
|
PROG
|
(PARI) pz(x)= sum(n=1, max(2, bitprecision(x)/x), my(a=moebius(n)); if(a!=0, a*log(zeta(n*x))/n));
Lichtman(n)=intnum(s=1, [oo, log(2)], exp(-sum(i=1, n, pz(i*s)*x^i/i)+O(x^(n+1)))-1)
Lichtman(20)
\\ Bill Allombert, Feb 14 2014 [via Artur Jasinski]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|