A340365 a(n) = A005940(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, 9, 1, 1, 1, 1, 1, 35, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 13, 1, 11, 1, 1, 1, 21, 1, 1, 35, 1, 1, 5, 1, 1, 1, 1, 1, 49, 1, 1, 1, 3, 1, 49, 1, 1, 9, 1, 1, 27, 1, 17, 13, 1, 1, 13, 11, 1, 1, 1, 1, 55, 1, 55, 21, 1, 1, 1, 1, 1, 35, 7, 1, 21, 1, 1, 5, 7, 1, 875, 1, 27, 1, 1, 1, 121

Offset: 1

Author

Antti Karttunen, Jan 06 2021

Keywords

• nonn

Comments

It is conjectured that A070776 gives the positions of all ones after the initial one. If that holds, then for all i, j: a(i) = a(j) => A340363(i) = A340363(j).

Links

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

Crossrefs

Cf. A005940, A070776, A324106, A340362, A340364, A340366.

Cf. also A305800, A340363.

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])); };
A340365(n) = { my(t=A005940(n)); t / gcd(t, A324106(n)); };

Formula

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