A342400 a(n) is the number of distinct sums of distinct unitary divisors of n.

1, 3, 3, 3, 3, 12, 3, 3, 3, 15, 3, 13, 3, 15, 15, 3, 3, 15, 3, 13, 15, 15, 3, 15, 3, 15, 3, 15, 3, 72, 3, 3, 15, 15, 15, 15, 3, 15, 15, 15, 3, 96, 3, 15, 15, 15, 3, 15, 3, 15, 15, 15, 3, 15, 15, 13, 15, 15, 3, 108, 3, 15, 15, 3, 15, 144, 3, 15, 15, 142, 3, 13

Offset: 1

Author

Amiram Eldar, Mar 10 2021

Keywords

• nonn

Links

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

Crossrefs

The unitary version of A119347.

Cf. A034448, A077610, A286652.

Programs

Mathematica

a[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &], x, s, m, c}, m = Length[d]; s = Plus @@ d; c = Rest@CoefficientList[Series[Product[1 + x^d[[i]], {i, 1, m}], {x, 0, s}], x]; Count[c, _?(# > 0 &)]]; Array[a, 100]

Formula

a(n) <= A034448(n) with equality if and only if n is a unitary practical number (A286652).

a(p^e) = 3 for a prime p and e >= 1.