A342400 - OEIS

%I #8 Mar 11 2021 03:32:17

%S 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,

%T 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,

%U 15,13,15,15,3,108,3,15,15,3,15,144,3,15,15,142,3,13

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

%H Amiram Eldar, <a href="/A342400/b342400.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t 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]

%Y The unitary version of A119347.

%Y Cf. A034448, A077610, A286652.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 10 2021