A348998 a(n) = A348928(A276086(n)), where A348928(n) = gcd(n, A003958(n)), and A003958 is multiplicative with a(p^e) = (p-1)^e, and A276086 gives the prime product form of primorial base expansion of n.

1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 3, 6, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18, 1, 2, 3, 6, 9, 18

Offset: 0

Author

Antti Karttunen, Nov 07 2021

Keywords

• nonn
• base
• look

Comments

After each primorial number (A002110), the apparent periodicity grows more complex.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A002110, A003958, A276086, A348928, A348999.

Programs

PARI

A348998(n) = { my(m1=1, m2=1, p=2); while(n, m1 *= (p^(n%p)); m2 *= ((p-1)^(n%p)); n = n\p; p = nextprime(1+p)); gcd(m1,m2); };