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A307826
The number of integers r such that all primes above a certain value have the form primorial(n)*q +- r.
1
1, 1, 4, 24, 240, 2880, 46080, 829440, 18247680, 510935040, 15328051200, 551809843200, 22072393728000, 927040536576000, 42643864682496000, 2217480963489792000, 128613895882407936000, 7716833752944476160000, 509311027694335426560000
OFFSET
1,3
LINKS
FORMULA
a(n) = Product_{k=1..n} A156037(k).
a(n) = A000010(A002110(n))/2 for n > 1.
a(n) = A005867(n)/2 for n > 1. - Alexandre Herrera, Apr 16 2023
EXAMPLE
For n=3, the third primorial is 2*3*5=30, and all primes at least 17 have the form 30n +- (1,7,11,13). So, a(3) = 4.
MATHEMATICA
a[1]=1; a[n_] := EulerPhi[Product[Prime[i], {i, 1, n}]]/2; Array[a, 20] (* Amiram Eldar, Jul 08 2019 *)
PROG
(Python)
import sympy
def A307826(n):
sympy.sieve.extend_to_no(n)
s = list(sympy.sieve._list)
prod = s[0]
print("1")
for i in range(1, n):
prod*=s[i]
print(sympy.ntheory.factor_.totient(prod)//2)
CROSSREFS
KEYWORD
nonn
AUTHOR
William Boyles, Apr 30 2019
STATUS
approved