A331184 Number of values of k, 1 <= k <= n, with A318310(k) = A318310(n).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 12 2020

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000120, A033879, A318310.

Cf. also A331181, A331183.

Programs

PARI

up_to = 16384;
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; };
A318310aux(n) = [hammingweight(n), (2*n) - sigma(n)];
v331184 = ordinal_transform(vector(up_to,n,A318310aux(n)));
A331184(n) = v331184[n];