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A340148 a(n) = Product_{distinct primes p dividing n} gcd(q-1, A003961(n)-1), where q = A151800(p), the next prime larger than p.

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%I A340148 #9 Dec 30 2020 20:00:33
%S A340148 1,2,4,2,6,4,10,2,4,4,12,8,16,4,4,2,18,4,22,4,4,4,28,4,6,4,4,4,30,16,
%T A340148 36,2,16,4,4,8,40,4,16,4,42,16,46,8,12,4,52,8,10,4,4,16,58,4,36,4,4,4,
%U A340148 60,8,66,4,4,2,4,8,70,4,16,40,72,4,78,4,8,4,4,8,82,4,4,4,88,8,36,4,4,4,96,16,4,8,16
%N A340148 a(n) = Product_{distinct primes p dividing n} gcd(q-1, A003961(n)-1), where q = A151800(p), the next prime larger than p.
%C A340148 Prime shifted analog of A063994.
%H A340148 Antti Karttunen, <a href="/A340148/b340148.txt">Table of n, a(n) for n = 1..8191</a>
%H A340148 Antti Karttunen, <a href="/A340148/a340148.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A340148 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A340148 a(n) = A063994(A003961(n)).
%F A340148 a(n) = A003972(n) / A340147(n).
%o A340148 (PARI)
%o A340148 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A340148 A063994(n) = { my(f=factor(n)[,1]); prod(i=1, #f, gcd(f[i]-1, n-1)); };
%o A340148 A340148(n) = A063994(A003961(n));
%o A340148 (PARI) A340148(n) = { my(f=factor(n)[,1], u=A003961(n)); prod(i=1, #f, gcd(nextprime(1+f[i])-1, u-1)); };
%o A340148 (PARI) A340148(n) = { my(u=A003961(n), f=factor(u)[,1]); prod(i=1, #f, gcd(f[i]-1, u-1)); };
%Y A340148 Cf. A003961, A003972, A063994, A340147.
%K A340148 nonn
%O A340148 1,2
%A A340148 _Antti Karttunen_, Dec 30 2020