A296089 - OEIS

%I #11 Dec 07 2017 22:19:26

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

%T 26,27,28,29,21,30,31,32,31,33,34,35,36,37,38,39,40,41,42,29,31,43,44,

%U 45,46,47,48,49,46,50,51,52,53,54,55,39,56,57,58,59,60,61,62,59,46,63,64,65,66,67,62,68,51,69,70,71,58,72,73,74,75,76,77,78,79,54,80,59,75

%N Filter combining the sum of divisors (A000203) and 2-adic valuation of n (A007814); restricted growth sequence transform of A286460.

%C This seems to be also the restricted growth sequence transform of A286359.

%C For all i, j:

%C   a(i) = a(j) => A296088(i) = A296088(j).

%H Antti Karttunen, <a href="/A296089/b296089.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 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o A000203(n) = sigma(n);

%o A001511(n) = (1+valuation(n,2));

%o A286460(n) = (1/2)*(2 + ((A001511(n)+A000203(n))^2) - A001511(n) - 3*A000203(n));

%o write_to_bfile(1,rgs_transform(vector(up_to,n,A286460(n))),"b296089.txt");

%Y Cf. A000203, A007814, A286359, A286460, A296088, A296090.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 07 2017