A200334 Decimal expansion of Sum_{n = 2 .. infinity }[ 1 / Sum {i=1..m} d(i)^n] where d(i) are the distinct prime divisors of n and m = omega(n) is the number of distinct prime divisors of n.

3, 5, 5, 0, 9, 3, 5, 7, 1, 9, 3, 0, 6, 7, 7, 6, 2, 3, 6, 2, 7, 3, 7, 6, 9, 0, 2, 2, 4, 3, 3, 8, 8, 8, 8, 8, 5, 8, 9, 0, 6, 1, 7, 3, 5, 8, 7, 9, 6, 8, 1, 0, 5, 2, 5, 4, 1, 3, 1, 3, 9, 9, 4, 4, 8, 7, 4, 3, 6, 9, 9, 3, 7, 8, 7, 8, 2, 3, 1, 3, 9, 7, 9, 8, 3, 5, 1, 2, 5, 1, 9, 1, 3, 1, 5, 8, 0, 7, 9, 3, 7, 1, 5, 8, 3

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Example

0.3550935719306776236273769022433888885890...

Maple

with(numtheory):Digits:=200:s:=0:for n from 2 to 2000 do:x:=factorset(n):p:=sum(‘x[i]^n’, ’i’=1..nops(x)): s:=s+evalf(1/p):od:print(s):

Mathematica

digits = 105; s[m_] := s[m] = Sum[f = FactorInteger[n][[All, 1]]; 1/Sum[p^n, {p, f}], {n, 2, m}] // RealDigits[#, 10, digits]& // First; s[digits] ; s[m = 2*digits]; While[s[m] != s[m/2], m = 2*m]; s[m] (* Jean-François Alcover, Feb 24 2014 *)

Prog

(PARI) sum(n=2, 1e3, f=factor(n)[, 1]; 1./sum(i=1, #f, f[i]^n)) \\ Charles R Greathouse IV, Nov 28 2011

Crossrefs

Sequence in context: A284867 A343955 A152416 * A138112 A106233 A366568

Adjacent sequences: A200331 A200332 A200333 * A200335 A200336 A200337

Keyword

nonn,cons

Author

Michel Lagneau, Nov 28 2011

Status

approved