A331180 Number of values of k, 1 <= k <= n, with A323910(k) = A323910(n), where A323910 is Dirichlet inverse of deficiency of n.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 3, 1, 2, 1, 4, 1, 1, 1, 3, 1, 1, 2, 4, 1, 1, 1, 4, 5, 1, 1, 2, 1, 3, 1, 5, 1, 5, 1, 6, 1, 1, 1, 6, 1, 1, 2, 6, 1, 2, 1, 7, 1, 3, 1, 2, 1, 2, 8, 9, 1, 1, 1, 3, 2, 2, 1, 3, 1, 1, 1, 7, 1, 10, 1, 11, 2, 1, 2, 1, 1, 2, 2, 7, 1, 1, 1, 8, 2

Offset

1,8

Comments

Ordinal transform of A323910.

Links

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

Mathematica

f[n_] := 2 n - DivisorSigma[1, n];
A323910[n_] := A323910[n] = If[n == 1, 1, -Sum[f[n/d] A323910[d], {d, Most@Divisors[n]}]];
Module[{b}, b[_] = 0; a[n_] := With[{t = A323910[n]}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 12 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; };
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A033879(n) = (2*n-sigma(n));
v331180 = ordinal_transform(DirInverse(vector(up_to, n, A033879(n))));
A331180(n) = v331180[n];

Crossrefs

Cf. A033879, A323910.

Cf. also A331178, A331181.

Sequence in context: A276153 A341348 A194606 * A126389 A278112 A286132

Adjacent sequences: A331177 A331178 A331179 * A331181 A331182 A331183

Keyword

nonn

Author

Antti Karttunen, Jan 11 2020

Status

approved