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A156542
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Number of distinct Sophie Germain prime factors of n.
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7
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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, 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, 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
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OFFSET
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1,6
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LINKS
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FORMULA
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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
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MAPLE
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with(numtheory): seq(add(pi(2*i+1)-pi(2*i), i in factorset(n)), n=1..100); # Ridouane Oudra, Aug 25 2019
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MATHEMATICA
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Join[{0}, Table[Count[FactorInteger[n][[All, 1]], _?(PrimeQ[2#+1]&)], {n, 2, 110}]] (* Harvey P. Dale, Apr 05 2020 *)
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PROG
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(Magma) [0] cat [&+[#PrimesInInterval(2*p, 2*p+1):p in PrimeDivisors(n)]:n in [2..100]]; // Marius A. Burtea, Aug 25 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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