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Cf. A003961, A020639, A276086, A355442, A284723 (even bisection), A355442, A355820, A355821 (positions of 1's).

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.

Antti Karttunen, <a href="/A355001/b355001.txt">Table of n, a(n) for n = 1..100000</a>

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allocatedSmallest common prime factor of A003961(n) and A276086(n), or 1 if forthey Anttiare Karttunencoprime.

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

1,2

<a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

<a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

a(n) = A020639(A355442(n)) = A020639(gcd(A003961(n), A276086(n))).

(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));

A355001(n) = A020639(A355442(n));

Cf. A003961, A020639, A276086, A355442, A284723 (even bisection).

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nonn

Antti Karttunen, Jul 13 2022

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