A351086 a(n) = gcd(A003415(n), A328572(n)), where A003415 is the arithmetic derivative and A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 35, 1, 1, 1, 1, 1, 49, 3, 1, 1, 7, 1, 7, 1, 7

Offset: 0

Author

Antti Karttunen, Feb 03 2022

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327858, A345000, A351084, A351085.

Programs

PARI

A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
A351086(n) = gcd(A003415(n), A328572(n));

PARI

A351086(n) = { my(m=1, p=2, orgn=A003415(n)); while(n, if(n%p, m *= (p^min((n%p)-1, valuation(orgn, p)))); n = n\p; p = nextprime(1+p)); (m); };

Formula

a(n) = gcd(A003415(n), A328572(n)).

a(n) = gcd(A327858(n), A345000(n)).