A332042 Number of integers whose Dedekind psi function (A001615) values are n.

1, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 9, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0

Offset: 1

Author

Amiram Eldar, Feb 05 2020

Keywords

• nonn

Examples

			a(6) = 2 since there are 2 solutions to psi(x) = 6: 4 and 5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001615, A054973, A063974, A065463, A332036, A332038, A332040.

Programs

Mathematica

psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); m = 100; v = Table[0, {m}]; Do[i = psi[k]; If[i <= m, v[[i]]++], {k, 1, m}]; v

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 - 1/(p*(p+1))) = 0.7044422... (A065463). - Amiram Eldar, Dec 25 2024