A351084 a(n) = gcd(n, A328572(n)), where 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, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 1, 1, 1, 7, 5, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 49, 1, 1, 1, 1, 1, 1, 35

Offset

0,16

Links

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

Index entries for sequences related to primorial base

Formula

a(n) = gcd(n, A328572(n)) = gcd(A324198(n), A351083(n)).

a(n) = gcd(n, A085731(A276086(n))) = gcd(n, A276086(n), A327860(n)).

Prog

(PARI)
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); };
A351084(n) = gcd(n, A328572(n));
(PARI) A351084(n) = { my(m=1, p=2, orgn=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, A324198, A327860, A328572, A351080, A351083.

Sequence in context: A129398 A109009 A060904 * A135469 A348735 A170817

Adjacent sequences: A351081 A351082 A351083 * A351085 A351086 A351087

Keyword

nonn,easy

Author

Antti Karttunen, Feb 03 2022

Status

approved