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%I #46 May 15 2023 08:42:58
%S 1,1,4,24,240,2880,46080,829440,18247680,510935040,15328051200,
%T 551809843200,22072393728000,927040536576000,42643864682496000,
%U 2217480963489792000,128613895882407936000,7716833752944476160000,509311027694335426560000
%N The number of integers r such that all primes above a certain value have the form primorial(n)*q +- r.
%H William Boyles, <a href="/A307826/b307826.txt">Table of n, a(n) for n = 1..350</a>
%F a(n) = Product_{k=1..n} A156037(k).
%F a(n) = A000010(A002110(n))/2 for n > 1.
%F a(n) = A005867(n)/2 for n > 1. - _Alexandre Herrera_, Apr 16 2023
%e 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.
%t a[1]=1; a[n_] := EulerPhi[Product[Prime[i], {i, 1, n}]]/2; Array[a, 20] (* _Amiram Eldar_, Jul 08 2019 *)
%o (Python)
%o import sympy
%o def A307826(n):
%o sympy.sieve.extend_to_no(n)
%o s = list(sympy.sieve._list)
%o prod = s[0]
%o print("1")
%o for i in range(1,n):
%o prod*=s[i]
%o print(sympy.ntheory.factor_.totient(prod)//2)
%Y Cf. A000010, A002110, A005867, A156037.
%K nonn
%O 1,3
%A _William Boyles_, Apr 30 2019
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