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

0,22

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to primorial base

Formula

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

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

Prog

(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); };

Crossrefs

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

Sequence in context: A334988 A334987 A222119 * A102280 A370239 A365403

Adjacent sequences: A351083 A351084 A351085 * A351087 A351088 A351089

Keyword

nonn,easy

Author

Antti Karttunen, Feb 03 2022

Status

approved