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 A279952 #26 Jan 01 2024 09:14:58
%S A279952 0,0,1,0,1,1,0,0,1,1,1,1,0,0,2,0,1,1,0,1,1,1,0,1,1,0,1,0,0,2,1,0,2,1,
%T A279952 1,1,0,0,1,1,1,1,0,1,2,0,0,1,0,1,2,0,0,1,2,0,1,0,1,2,0,1,1,0,1,2,1,1,
%U A279952 1,1,0,1,0,0,2,0,1,1,0,1,1,1,1,1,2,0,1,1,0,2,0,0,2,0,1,1,0,0,2,1,0,2,0,0,2,0,0,1,1,2,1,0,0,1,1,0,1,1,1,2
%N A279952 Number of primes with prime subscripts dividing n.
%H A279952 G. C. Greubel, <a href="/A279952/b279952.txt">Table of n, a(n) for n = 1..5000</a>
%F A279952 G.f.: Sum_{k>=1} x^prime(prime(k))/(1 - x^prime(prime(k))).
%F A279952 a(n) = Sum_{d|n} A111406(d-1). - _Ridouane Oudra_, Sep 12 2023
%F A279952 Additive with a(p^e) = 1 if primepi(p) is prime, and 0 otherwise. - _Amiram Eldar_, Nov 03 2023
%F A279952 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{n>=1} 1/A006450(n) = 1.04... (see A006450 for a better estimate of this constant). - _Amiram Eldar_, Jan 01 2024
%e A279952 a(15) = 2 because 15 has 4 divisors {1,3,5,15} among which 2 divisors {3,5} are primes with prime subscripts.
%p A279952 with(numtheory): seq(add(pi(pi(d))-pi(pi(d-1)), d in divisors(n)), n=1..80); # _Ridouane Oudra_, Sep 12 2023
%t A279952 Rest[nmax = 120; CoefficientList[Series[Sum[x^Prime[Prime[k]]/(1 - x^Prime[Prime[k]]), {k, 1, nmax}], {x, 0, nmax}], x]]
%t A279952 f[p_, e_] := If[PrimeQ[PrimePi[p]], 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 03 2023 *)
%o A279952 (PARI) my(x='x+O('x^120)); concat([0, 0], Vec(sum(k=1, 120, x^prime(prime(k))/(1 - x^prime(prime(k)))))) \\ _Indranil Ghosh_, May 23 2017
%Y A279952 Cf. A001221, A006450, A257994.
%Y A279952 Cf. A000720, A111406.
%K A279952 nonn,easy
%O A279952 1,15
%A A279952 _Ilya Gutkovskiy_, Dec 23 2016