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 A354950 #14 Jun 14 2022 21:40:11
%S A354950 0,1,1,1,2,2,3,7,4,9,20,31,57,88,139,282,421,806,1397,2572,4440,7863,
%T A354950 14580,26211,47727,86929,159972,292650,542477,1000087,1850347,3432551,
%U A354950 6381199
%N A354950 The number of squarefree numbers whose largest prime divisor is prime(n) and that are averages of twin prime pairs.
%F A354950 Conjecture: Limit_{n->oo} log(a(n))/(n*log(n)) = c ~ 0.13... .
%e A354950 n prime(n) a(n) terms k of A070195 with A006530(k) = prime(n)
%e A354950 - -------- ---- ---------------------------------------------
%e A354950 1 2 0 -
%e A354950 2 3 1 6
%e A354950 3 5 1 30
%e A354950 4 7 1 42
%e A354950 5 11 2 462, 2310
%e A354950 6 13 2 858, 2730
%e A354950 7 17 3 102, 9282, 102102
%e A354950 8 19 7 570, 1482, 6270, 21318, 43890, 51870, 1939938
%t A354950 a[n_] := Count[Prime[n] * Divisors[Product[Prime[i], {i, 1, n - 1}]], _?(PrimeQ[# - 1] && PrimeQ[# + 1] &)]; Array[a, 10]
%o A354950 (Python)
%o A354950 from math import prod
%o A354950 from itertools import combinations
%o A354950 from sympy import primerange, prime, isprime
%o A354950 def A354950(n):
%o A354950 plist = list(primerange(2,p:=prime(n)))
%o A354950 return sum(1 for l in range(1,n) for d in combinations(plist,l) if isprime((q:= prod(d)*p)-1) and isprime(q+1)) # _Chai Wah Wu_, Jun 14 2022
%Y A354950 Cf. A005117, A006530, A014574, A070195, A354951.
%K A354950 nonn,more
%O A354950 1,5
%A A354950 _Amiram Eldar_, Jun 13 2022