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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.
2
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, 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, 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
OFFSET
1,2
COMMENTS
Prime shifted analog of A063994.
FORMULA
a(n) = A063994(A003961(n)).
a(n) = A003972(n) / A340147(n).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A063994(n) = { my(f=factor(n)[, 1]); prod(i=1, #f, gcd(f[i]-1, n-1)); };
(PARI) A340148(n) = { my(f=factor(n)[, 1], u=A003961(n)); prod(i=1, #f, gcd(nextprime(1+f[i])-1, u-1)); };
(PARI) A340148(n) = { my(u=A003961(n), f=factor(u)[, 1]); prod(i=1, #f, gcd(f[i]-1, u-1)); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 30 2020
STATUS
approved