A322020 a(n) = Product_{d|n, gcd(d,n/d) is a prime power} gcd(d,n/d).

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 4, 1, 1, 1, 16, 1, 9, 1, 4, 1, 1, 1, 16, 5, 1, 9, 4, 1, 1, 1, 64, 1, 1, 1, 36, 1, 1, 1, 16, 1, 1, 1, 4, 9, 1, 1, 256, 7, 25, 1, 4, 1, 81, 1, 16, 1, 1, 1, 16, 1, 1, 9, 512, 1, 1, 1, 4, 1, 1, 1, 144, 1, 1, 25, 4, 1, 1, 1, 256, 81, 1, 1, 16, 1, 1, 1, 16, 1, 81, 1, 4, 1, 1, 1, 4096, 1, 49, 9, 100, 1, 1, 1, 16, 1

Offset: 1

Author

Antti Karttunen, Nov 28 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A069513, A294876, A295666.

Programs

PARI

A322020(n) = { my(m=1,p); fordiv(n, d, p = gcd(d, n/d); if(isprimepower(p), m *= p)); m; };

Formula

a(n) = Product_{d|n} gcd(d,n/d)^A069513(gcd(d,n/d)).