|
%I #19 Jun 12 2021 09:08:45
%S 0,0,0,0,0,3,0,0,0,8,0,6,0,11,3,0,0,16,0,13,6,19,0,15,0,24,0,35,0,9,0,
%T 0,9,32,10,48,0,35,12,45,0,16,0,38,23,43,0,30,0,48,15,45,0,51,30,42,
%U 18,56,0,41,0,59,21,0,23,49,0,96,21,52,0,57,0,72,24,70,39,60,0,60,0,80,0,36,30,83,27,118,0,61,59,131
%N a(n) = A344875(n) - A011772(n).
%C Apparently A000961 gives the positions of zeros.
%H Antti Karttunen, <a href="/A344876/b344876.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A344876/a344876.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = A344875(n) - A011772(n).
%F a(n) >= A344976(n).
%t A011772[n_] := Module[{m = 1}, While[Not[IntegerQ[m(m+1)/(2n)]], m++]; m];
%t A344875[n_] := Product[{p, e} = pe; If[p == 2, 2^(1+e)-1, p^e-1], {pe, FactorInteger[n]}];
%t a[n_] := If[n == 1, 0, A344875[n] - A011772[n]];
%t Array[a, 100] (* _Jean-François Alcover_, Jun 12 2021 *)
%o (PARI)
%o 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 A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
%o A344876(n) = (A344875(n)-A011772(n));
%Y Cf. A000961, A011772, A344875, A344969, A344973, A344976.
%Y Cf. also A344763, A344765, A344874.
%K nonn,look
%O 1,6
%A _Antti Karttunen_, Jun 03 2021
|
