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Number of values of k, 1 <= k <= n, with A318310(k) = A318310(n).
3

%I #9 Jan 12 2020 23:51:13

%S 1,2,1,3,1,1,1,4,1,2,1,1,1,1,1,5,1,1,1,1,2,1,1,1,1,3,1,1,1,1,1,6,1,1,

%T 1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,7,1,2,1,1,

%U 1,1,1,1,1,1,2,2,1,3,1,1,2,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,1,4,1,1,1

%N Number of values of k, 1 <= k <= n, with A318310(k) = A318310(n).

%C Ordinal transform of A318310, or equally, of the ordered pair [A000120(n), A033879(n)], i.e., binary weight of n & deficiency of n.

%H Antti Karttunen, <a href="/A331184/b331184.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%o (PARI) up_to = 16384;

%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };

%o A318310aux(n) = [hammingweight(n), (2*n) - sigma(n)];

%o v331184 = ordinal_transform(vector(up_to,n,A318310aux(n)));

%o A331184(n) = v331184[n];

%Y Cf. A000120, A033879, A318310.

%Y Cf. also A331181, A331183.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 12 2020