A346469 -id:A346469 - cp's OEIS frontend

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

Antti Karttunen, Jul 21 2021

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

Cf. also A346469.

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));

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

A345930 a(n) = A344756(A276086(n)).

Original entry on oeis.org

1, 1, 1, 2, 7, 1, 1, 1, 1, 13, 41, 2, 9, 11, 37, 2, 47, 3, 11, 7, 43, 19, 53, 4, 13, 17, 49, 11, 59, 1, 1, 1, 1, 17, 55, 1, 1, 1, 1, 106, 317, 19, 73, 92, 289, 127, 359, 13, 87, 113, 331, 148, 401, 11, 101, 134, 373, 169, 443, 2, 11, 13, 47, 2, 61, 17, 69, 86, 277, 121, 347, 2, 83, 107, 319, 2, 389, 31, 97, 128, 19

Offset: 1

Antti Karttunen, Jul 19 2021

Antti Karttunen, Table of n, a(n) for n = 1..13860
Index entries for sequences related to primorial base

Cf. A003415, A069359, A276086, A327860, A329029, A344756, A346469.

Cf. also A342002, A346474, A346475 (compare the scatter plots).

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A344756(n) = { my(u=A003415(n)); (u/gcd(u,A069359(n))); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345930(n) = A344756(A276086(n));

a(n) = A344756(A276086(n)).

a(n) = A327860(n) / A346469(n) = A327860(n) / gcd(A327860(n), A329029(n)).

cp's OEIS Frontend

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.

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