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%I #22 Sep 08 2022 08:45:41
%S 0,1,1,1,1,2,0,1,1,2,1,2,0,1,2,1,0,2,0,2,1,2,1,2,1,1,1,1,1,3,0,1,2,1,
%T 1,2,0,1,1,2,1,2,0,2,2,2,0,2,0,2,1,1,1,2,2,1,1,2,0,3,0,1,1,1,1,3,0,1,
%U 2,2,0,2,0,1,2,1,1,2,0,2,1,2,1,2,1,1,2,2,1,3,0,2,1,1,1,2,0,1,2,2,0,2,0,1,2
%N Number of distinct Sophie Germain prime factors of n.
%H Reinhard Zumkeller, <a href="/A156542/b156542.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) <= A001221(n));
%F a(A156541(n)) = A001221(A156541(n)); a(A156543(n)) = 0;
%F a(A005384(n)) = 1; a(A053176(n)) = 0.
%F a(n) = Sum_{p|n} (pi(2p+1) - pi(2p)), where p is a prime and pi(k) = A000720(k). - _Ridouane Oudra_, Aug 25 2019
%p with(numtheory): seq(add(pi(2*i+1)-pi(2*i), i in factorset(n)), n=1..100); # _Ridouane Oudra_, Aug 25 2019
%t Join[{0},Table[Count[FactorInteger[n][[All,1]],_?(PrimeQ[2#+1]&)],{n,2,110}]] (* _Harvey P. Dale_, Apr 05 2020 *)
%o (Magma) [0] cat [&+[#PrimesInInterval(2*p,2*p+1):p in PrimeDivisors(n)]:n in [2..100]]; // _Marius A. Burtea_, Aug 25 2019
%Y Cf. A000720, A001221, A005384, A053176, A156541, A156543.
%K nonn
%O 1,6
%A _Reinhard Zumkeller_, Feb 10 2009
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