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 A156542 Number of distinct Sophie Germain prime factors of n. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) <= A001221(n)); a(A156541(n)) = A001221(A156541(n)); a(A156543(n)) = 0; a(A005384(n)) = 1; a(A053176(n)) = 0. 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 MAPLE with(numtheory): seq(add(pi(2*i+1)-pi(2*i), i in factorset(n)), n=1..100); # Ridouane Oudra, Aug 25 2019 MATHEMATICA Join[{0}, Table[Count[FactorInteger[n][[All, 1]], _?(PrimeQ[2#+1]&)], {n, 2, 110}]] (* Harvey P. Dale, Apr 05 2020 *) PROG (MAGMA) [0] cat [&+[#PrimesInInterval(2*p, 2*p+1):p in PrimeDivisors(n)]:n in [2..100]]; // Marius A. Burtea, Aug 25 2019 CROSSREFS Cf. A000720, A001221, A005384, A053176, A156541, A156543. Sequence in context: A025911 A060184 A055639 * A307990 A066360 A061358 Adjacent sequences:  A156539 A156540 A156541 * A156543 A156544 A156545 KEYWORD nonn AUTHOR Reinhard Zumkeller, Feb 10 2009 STATUS approved

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Last modified April 10 14:07 EDT 2021. Contains 342845 sequences. (Running on oeis4.)