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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.
0
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
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
KEYWORD
nonn,cons
AUTHOR
Michel Lagneau, Nov 28 2011
STATUS
approved