A324938 a(n) = the number of values of m such that the sum of proper unitary divisors of m (A034460) is n.

0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 3, 1, 3, 2, 3, 3, 2, 2, 3, 3, 4, 3, 2, 3, 3, 3, 4, 4, 3, 3, 3, 5, 4, 5, 4, 5, 2, 4, 4, 5, 4, 5, 3, 5, 5, 5, 2, 6, 3, 6, 4, 6, 3, 7, 3, 6, 4, 5, 3, 7, 3, 5, 4, 6, 2, 8, 2, 6, 5, 7, 2, 8, 4, 6, 7, 7, 4, 9, 2, 7, 4, 5, 4, 9, 3, 9

Offset: 2

Author

Amiram Eldar, Sep 05 2019

Keywords

• nonn

Comments

The unitary version of A048138.

The offset is 2 as in A048138 since there are infinitely many numbers (all the powers of primes) for which A034460 = 1.

Examples

			a(8) = 2 since 8 is the sum of the proper unitary divisors of 10 (1 + 2 + 5) and 12 (1 + 3 + 4).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A034448, A034460, A048138, A063948.

Programs

Mathematica

us[1] = 0; us[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - n;  m = 100; v = Table[0, {m}]; Do[u = us[k]; If[2 <= u <= m, v[[u]]++], {k, 1, m^2}]; Rest @ v

Formula

a(A063948(n)) = 0.