A340365 - OEIS

%I #6 Jan 06 2021 17:48:43

%S 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,

%T 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,

%U 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

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

%C 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).

%H Antti Karttunen, <a href="/A340365/b340365.txt">Table of n, a(n) for n = 1..16384</a>

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

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A324106(n) = { my(f=factor(n)); prod(i=1, #f~, A005940(f[i,1]^f[i,2])); };

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

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

%Y Cf. also A305800, A340363.

%K nonn

%O 1,15

%A _Antti Karttunen_, Jan 06 2021