A344698 a(n) = A344696(A108951(n)).

1, 1, 1, 7, 1, 7, 1, 5, 91, 7, 1, 5, 1, 7, 91, 31, 1, 65, 1, 5, 91, 7, 1, 31, 2821, 7, 25, 5, 1, 65, 1, 21, 91, 7, 2821, 403, 1, 7, 91, 31, 1, 65, 1, 5, 25, 7, 1, 21, 7657, 403, 91, 5, 1, 155, 2821, 31, 91, 7, 1, 403, 1, 7, 25, 127, 2821, 65, 1, 5, 91, 403, 1, 91, 1, 7, 155, 5, 7657, 65, 1, 21, 3751, 7, 1, 403, 2821

Offset: 1

Author

Antti Karttunen, May 26 2021

Keywords

• nonn

Comments

Records seem to occur on certain squares: 1, 4, 9, 25, 49, 100, 121, 289, 361, 529, 841, 961, etc. See A344701.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10201
• Index entries for sequences related to primorial numbers
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A001615, A108951, A337203, A344696, A344699, A344701 (positions of records).

Programs

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
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
A344696(n) = { my(u=sigma(n)); (u/gcd(u,A001615(n))); };
A344698(n) = A344696(A108951(n));