cp's OEIS Frontend

A344971 a(n) = A344875(n) / gcd(A011772(n), A344875(n)).

%I A344971 #13 Jun 30 2021 19:48:48
%S A344971 1,1,1,1,1,2,1,1,1,3,1,7,1,18,8,1,1,3,1,28,2,30,1,2,1,3,1,6,1,8,1,1,
%T A344971 20,3,12,7,1,54,2,4,1,9,1,35,32,66,1,31,1,3,32,28,1,26,4,15,2,3,1,56,
%U A344971 1,90,16,1,48,60,1,7,44,18,1,40,1,3,2,9,20,6,1,31,1,3,1,7,32,126,56,75,1,96,72,154,2,138,72
%N A344971 a(n) = A344875(n) / gcd(A011772(n), A344875(n)).
%C A344971 Numerator of the ratio A344875(n)/A011772(n): 1/1, 3/3, 2/2, 7/7, 4/4, 6/3, 6/6, 15/15, 8/8, 12/4, 10/10, 14/8, 12/12, 18/7, 8/5, 31/31, 16/16, 24/8, 18/18, 28/15, 12/6, 30/11, ... = 1/1, 1/1, 1/1, 1/1, 1/1, 2/1, 1/1, 1/1, 1/1, 3/1, 1/1, 7/4, 1/1, 18/7, 8/5, 1/1, 1/1, 3/1, 1/1, 28/15, 2/1, 30/11, etc.
%H A344971 Antti Karttunen, <a href="/A344971/b344971.txt">Table of n, a(n) for n = 1..16384</a>
%H A344971 Antti Karttunen, <a href="/A344971/a344971.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A344971 a(n) = A344875(n) / A344969(n) = A344875(n) / gcd(A011772(n), A344875(n)).
%o A344971 (PARI)
%o A344971 A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
%o A344971 A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
%o A344971 A344971(n) = { my(u=A344875(n)); (u/gcd(u, A011772(n))); };
%Y A344971 Cf. A011772, A344875, A344969, A344970 (denominators), A344972 (ratio A344875/A011772 floored down), A344973 (and their remainder).
%K A344971 nonn,frac
%O A344971 1,6
%A A344971 _Antti Karttunen_, Jun 04 2021