This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156542 #30 Sep 03 2024 22:09:21
%S A156542 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 A156542 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 A156542 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 A156542 Number of distinct Sophie Germain prime factors of n.
%H A156542 Reinhard Zumkeller, <a href="/A156542/b156542.txt">Table of n, a(n) for n = 1..10000</a>
%F A156542 a(n) <= A001221(n).
%F A156542 a(A156541(n)) = A001221(A156541(n)); a(A156543(n)) = 0.
%F A156542 a(A005384(n)) = 1; a(A053176(n)) = 0.
%F A156542 a(n) = Sum_{p|n} A101264(p), where p is a prime. - _Ridouane Oudra_, Aug 25 2019
%F A156542 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} 1/A005384(k) (see A005384 for an estimate of this sum). - _Amiram Eldar_, Jun 03 2024
%p A156542 with(numtheory): A101264:=p-> pi(2*p+1)-pi(2*p): seq(add(A101264(p), p in factorset(n)), n=1..100); # _Ridouane Oudra_, Aug 25 2019
%t A156542 Join[{0},Table[Count[FactorInteger[n][[All,1]],_?(PrimeQ[2#+1]&)],{n,2,110}]] (* _Harvey P. Dale_, Apr 05 2020 *)
%o A156542 (Magma) [0] cat [&+[#PrimesInInterval(2*p,2*p+1):p in PrimeDivisors(n)]:n in [2..100]]; // _Marius A. Burtea_, Aug 25 2019
%Y A156542 Cf. A000720, A001221, A005384, A053176, A156541, A156543, A101264.
%K A156542 nonn
%O A156542 1,6
%A A156542 _Reinhard Zumkeller_, Feb 10 2009