A331181 Number of values of k, 1 <= k <= n, with A033879(k) = A033879(n), where A033879(n) is the deficiency of n, 2n-sigma(n).

1, 2, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 1, 2, 2, 5, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 6, 2, 2, 2, 1, 1, 2, 3, 1, 1, 3, 1, 3, 2, 1, 1, 1, 1, 1, 2, 3, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 4, 7, 2, 5, 1, 4, 2, 2, 1, 1, 1, 2, 2, 3, 2, 6, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 3, 3, 1, 3, 1, 1, 1, 3, 1, 1, 7, 1, 2, 3

Offset

1,2

Comments

Ordinal transform of A033879, or equally, of A033880, or of A286449.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Mathematica

b[_] = 0;
a[n_] := With[{t = 2 n - DivisorSigma[1, n]}, b[t] = b[t] + 1];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

Prog

(PARI)
up_to = 65537;
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; };
A033879(n) = (2*n-sigma(n));
v331181 = ordinal_transform(vector(up_to, n, A033879(n)));
A331181(n) = v331181[n];

Crossrefs

Cf. A000203, A033879, A033880, A286449.

Cf. also A331180, A331182.

Sequence in context: A331184 A333768 A306922 * A344593 A353278 A328917

Adjacent sequences: A331178 A331179 A331180 * A331182 A331183 A331184

Keyword

nonn

Author

Antti Karttunen, Jan 11 2020

Status

approved