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%I #20 Feb 24 2014 06:55:38
%S 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,
%T 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,
%U 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
%N 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.
%e 0.3550935719306776236273769022433888885890...
%p 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):
%t 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 *)
%o (PARI) sum(n=2,1e3,f=factor(n)[,1];1./sum(i=1,#f,f[i]^n)) \\ _Charles R Greathouse IV_, Nov 28 2011
%K nonn,cons
%O 0,1
%A _Michel Lagneau_, Nov 28 2011
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