cp's OEIS Frontend

A344972 a(n) = floor(A344875(n) / A011772(n)).

%I A344972 #9 Jun 20 2021 19:19:14
%S A344972 1,1,1,1,1,2,1,1,1,3,1,1,1,2,1,1,1,3,1,1,2,2,1,2,1,3,1,6,1,1,1,1,1,3,
%T A344972 1,7,1,2,2,4,1,1,1,2,3,2,1,1,1,3,1,2,1,2,4,1,2,3,1,3,1,2,1,1,1,5,1,7,
%U A344972 1,3,1,1,1,3,2,2,2,6,1,1,1,3,1,1,1,2,1,4,1,2,5,6,2,2,3,2,1,3,1,7,1,1,1,2,3
%N A344972 a(n) = floor(A344875(n) / A011772(n)).
%H A344972 Antti Karttunen, <a href="/A344972/b344972.txt">Table of n, a(n) for n = 1..65537</a>
%F A344972 a(n) = (A344875(n)-A344973(n)) / A011772(n) = floor(A344875(n) / A011772(n)).
%F A344972 a(n) = floor(A344971(n) / A344970(n)). - _Antti Karttunen_, Jun 20 2021
%o A344972 (PARI)
%o A344972 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 A344972 A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
%o A344972 A344972(n) = floor(A344875(n)/A011772(n));
%Y A344972 Cf. A011772, A344875, A344876, A344969, A344970, A344971, A344973.
%K A344972 nonn
%O A344972 1,6
%A A344972 _Antti Karttunen_, Jun 04 2021