A340366 a(n) = A324106(n) / gcd(A005940(n), A324106(n)), where A324106(n) is multiplicative with a(p^e) = A005940(p^e).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 45, 1, 15, 1, 1, 1, 25, 1, 1, 27, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 9, 1, 1, 5, 1, 1, 7, 1, 125, 45, 1, 1, 27, 15, 1, 1, 1, 1, 49, 1, 27, 25, 1, 1, 1, 1, 1, 27, 1, 1, 25, 1, 1, 1, 3, 1, 243, 1, 7, 1, 1, 1, 35, 1, 1, 11

Offset: 1

Author

Antti Karttunen, Jan 06 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A005940, A324106, A340364, A340365.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A324106(n) = { my(f=factor(n)); prod(i=1, #f~, A005940(f[i,1]^f[i,2])); };
A340366(n) = { my(u=A324106(n)); (u / gcd(u, A005940(n))); };

Formula

a(n) = A324106(n) / A340364(n) = A324106(n) / gcd(A005940(n), A324106(n)).