A330749 a(n) = gcd(n, A064989(n)), where A064989 is fully multiplicative with a(2) = 1 and a(prime(k)) = prime(k-1) for odd primes.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 5, 4, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 4, 1, 1, 3, 1, 7, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 15

Offset: 1

Author

Antti Karttunen, Dec 29 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A064989, A319626, A322361.

Programs

PARI

A330749(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); gcd(n,factorback(f)); };

Formula

a(n) = gcd(n, A064989(n)).

a(n) = n / A319626(n).

a(n) = A064989(A322361(n)).