A353667 a(n) = n / gcd(n, A351546(n)).

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 3, 13, 7, 5, 16, 17, 18, 19, 10, 21, 11, 23, 6, 25, 13, 27, 1, 29, 15, 31, 32, 11, 17, 35, 36, 37, 19, 39, 4, 41, 21, 43, 11, 15, 23, 47, 12, 49, 50, 17, 26, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 64, 65, 33, 67, 34, 23, 35, 71, 72, 73, 37, 75, 19, 77, 39, 79, 40, 81, 41, 83, 3

Offset: 1

Author

Antti Karttunen, May 04 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A351546, A353666, A353668.

Differs from A098988 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])); };
A353667(n) = (n / gcd(n, A351546(n)));

Formula

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