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a(n) is the number of divisors of n which are Loeschian numbers (A003136).
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%I #6 Oct 10 2024 16:03:43

%S 1,1,2,2,1,2,2,2,3,1,1,4,2,2,2,3,1,3,2,2,4,1,1,4,2,2,4,4,1,2,2,3,2,1,

%T 2,6,2,2,4,2,1,4,2,2,3,1,1,6,3,2,2,4,1,4,1,4,4,1,1,4,2,2,6,4,2,2,2,2,

%U 2,2,1,6,2,2,4,4,2,4,2,3,5,1,1,8,1,2,2,2

%N a(n) is the number of divisors of n which are Loeschian numbers (A003136).

%e a(1) = 1 because 1 has only one divisor 1 = A003136(2).

%e a(3) = 2 because 3 has divisors 1 = A003136(2) and 3 = A003136(3).

%e a(9) = 3 because 9 has the divisors 1 = A003136(2), 3 = A003136(3) and 9 = A003136(6).

%o (Magma) f:=func<n|NormEquation(3, n) eq true>; [#[d:d in Divisors(n)|f(d)]:n in [1..150]];

%Y Cf. A003136.

%K nonn

%O 1,3

%A _Marius A. Burtea_, Sep 15 2024