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 A354950 The number of squarefree numbers whose largest prime divisor is prime(n) and that are averages of twin prime pairs. 2
 0, 1, 1, 1, 2, 2, 3, 7, 4, 9, 20, 31, 57, 88, 139, 282, 421, 806, 1397, 2572, 4440, 7863, 14580, 26211, 47727, 86929, 159972, 292650, 542477, 1000087, 1850347, 3432551, 6381199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Table of n, a(n) for n=1..33. FORMULA Conjecture: Limit_{n->oo} log(a(n))/(n*log(n)) = c ~ 0.13... . EXAMPLE n prime(n) a(n) terms k of A070195 with A006530(k) = prime(n) - -------- ---- --------------------------------------------- 1 2 0 - 2 3 1 6 3 5 1 30 4 7 1 42 5 11 2 462, 2310 6 13 2 858, 2730 7 17 3 102, 9282, 102102 8 19 7 570, 1482, 6270, 21318, 43890, 51870, 1939938 MATHEMATICA a[n_] := Count[Prime[n] * Divisors[Product[Prime[i], {i, 1, n - 1}]], _?(PrimeQ[# - 1] && PrimeQ[# + 1] &)]; Array[a, 10] PROG (Python) from math import prod from itertools import combinations from sympy import primerange, prime, isprime def A354950(n): plist = list(primerange(2, p:=prime(n))) 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 CROSSREFS Cf. A005117, A006530, A014574, A070195, A354951. Sequence in context: A210753 A208762 A209746 * A267822 A210598 A330728 Adjacent sequences: A354947 A354948 A354949 * A354951 A354952 A354953 KEYWORD nonn,more AUTHOR Amiram Eldar, Jun 13 2022 STATUS approved

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Last modified February 22 02:45 EST 2024. Contains 370239 sequences. (Running on oeis4.)