A353666 a(n) = gcd(n, A351546(n)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 28, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 2, 1, 4, 3, 2, 1, 4, 1, 1, 3, 2, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 2, 3, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 28, 1, 2, 3, 4, 1, 2, 7, 4, 1, 2, 5, 4, 1, 1, 3, 1, 1, 2, 1, 2, 3

Offset: 1

Author

Antti Karttunen, May 04 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A351546, A353667, A353668.

Differs from A353688 for the first time at n = 28, 30, 40, 60, 66, 84, 90, 102, 120, ...

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351546(n) = { my(f=factor(sigma(n)), u=A003961(n)); prod(k=1, #f~, f[k, 1]^((0!=(u%f[k, 1]))*f[k, 2])); };
A353666(n) = gcd(n, A351546(n));

Formula

a(n) = gcd(n, A351546(n)).

a(n) = n / A353667(n) = A351546(n) / A353668(n).