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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
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
Sequence in context: A210753 A208762 A209746 * A267822 A210598 A330728
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.)