login
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.
6
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
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); };
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Feb 03 2022
STATUS
approved