|
%I #6 Jan 08 2019 19:08:26
%S 1,2,3,4,3,5,3,6,3,7,3,8,3,9,3,10,3,11,3,12,3,13,3,14,3,15,3,16,3,17,
%T 3,18,3,19,3,20,3,21,3,22,3,15,3,23,3,24,3,25,3,26,3,27,3,28,3,29,3,
%U 30,3,31,3,32,3,33,3,34,3,35,3,36,3,37,3,38,3,39,3,36,3,40,3,41,3,27,3,42,3,43,3,44,3,45,3,46,3,47,3,48,3,49,3,50,3,51,3
%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A291756(n) for all n, except f(1) = -1 and for odd numbers n > 1, f(n) = 0.
%C For all i, j:
%C A319701(i) = A319701(j) => a(i) = a(j) => A319998(i) = A319998(j).
%H Antti Karttunen, <a href="/A323237/b323237.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ From A173557
%o Aux323237(n) = if(1==n,-1,if(n%2,0,(1/2)*(2 + ((A003557(n)+A173557(n))^2) - A003557(n) - 3*A173557(n))));
%o v323237 = rgs_transform(vector(up_to, n, Aux323237(n)));
%o A323237(n) = v323237[n];
%Y Cf. A003557, A173557, A291756, A295887, A319701, A319998, A322587, A323238, A323241.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 08 2019
|
