%I #8 Dec 04 2017 12:09:53

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,21,

%T 26,27,28,29,30,31,32,33,34,35,36,37,34,38,39,13,40,41,42,43,44,45,46,

%U 47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,54,71,72,73,67,74,75,76,52,77,78,79,80,81,82,83,84,85,86,73

%N Filter-sequence combining A003557(n) and A023900(n).

%C For all i, j: a(i) = a(j) => A295887(i) = A295887(j).

%H Antti Karttunen, <a href="/A295886/b295886.txt">Table of n, a(n) for n = 1..65537</a>

%F Restricted growth sequence transform of sequence a(n) = (1/2)*(2 + ((A003557(n) + A295876(n))^2) - A003557(n) - 3*A295876(n)).

%o (PARI)

%o allocatemem(2^30);

%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 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0,f[i, 2]-1)); factorback(f); };

%o A023900(n) = sumdivmult(n, d, d*moebius(d)); \\ This function from _Charles R Greathouse IV_, Sep 09 2014

%o v295876 = rgs_transform(vector(up_to,n,A023900(n)))

%o A295876(n) = v295876[n];

%o Anotsubmitted6(n) = (1/2)*(2 + ((A003557(n)+A295876(n))^2) - A003557(n) - 3*A295876(n));

%o write_to_bfile(1,rgs_transform(vector(up_to,n,Anotsubmitted6(n))),"b295886.txt");

%Y Cf. A003557, A023900, A295876, A295887.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 03 2017