A346471 a(n) = A344695(A276086(n)), where A344695(x) = gcd(psi(x), sigma(x)), and A276086 gives the prime product form of primorial base expansion of n.

1, 3, 4, 12, 1, 3, 6, 18, 24, 72, 6, 18, 1, 3, 4, 12, 1, 3, 6, 18, 24, 72, 12, 36, 1, 3, 4, 12, 1, 3, 8, 24, 32, 96, 8, 24, 48, 144, 192, 576, 48, 144, 8, 24, 32, 96, 8, 24, 48, 144, 192, 576, 96, 288, 8, 24, 32, 96, 8, 24, 1, 3, 4, 12, 3, 9, 6, 18, 24, 72, 18, 54, 3, 9, 12, 36, 3, 9, 12, 36, 48, 144, 36, 108, 3, 9, 12, 36

Offset: 0

Author

Antti Karttunen, Jul 21 2021

Keywords

• nonn
• base
• look

Links

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

Crossrefs

Cf. A000203, A001615, A276086, A324653, A344695, A346470.

Cf. also A346469.

Programs

PARI

A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A344695(n) = gcd(sigma(n), A001615(n));
A346471(n) = A344695(A276086(n));

Formula

a(n) = A344695(A276086(n)) = gcd(A324653(n), A346470(n)).