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A355001
Smallest common prime factor of A003961(n) and A276086(n), or 1 if they are coprime, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
5
1, 3, 1, 3, 1, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 7, 1, 3, 1, 3, 7, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 7, 3, 5, 3, 1, 7, 1, 3, 1, 3, 7, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5, 3, 1, 5, 7, 3, 5, 3, 1, 7, 1, 3, 1, 3, 7, 5, 1, 3, 5, 3, 1, 5, 1, 3, 5
OFFSET
1,2
FORMULA
a(n) = A020639(A355442(n)) = A020639(gcd(A003961(n), A276086(n))).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355442(n) = gcd(A003961(n), A276086(n));
CROSSREFS
Cf. A003961, A020639, A276086, A284723 (even bisection), A355442, A355820, A355821 (positions of 1's).
Sequence in context: A293485 A250207 A216319 * A337713 A309425 A218355
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 13 2022
STATUS
approved