cp's OEIS Frontend

A330757 Let d(1) < d(2) < ... < d(q) denote the divisors of n; a(n) is the number of elements of the set { d(1)/d(2), d(2)/d(3), ..., d(q-1)/d(q) }.

%I A330757 #6 Jan 02 2020 13:31:35
%S A330757 0,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,2,1,2,2,2,1,3,1,2,1,2,1,4,1,1,2,2,
%T A330757 2,3,1,2,2,3,1,3,1,2,3,2,1,3,1,2,2,2,1,2,2,3,2,2,1,6,1,2,3,1,2,3,1,2,
%U A330757 2,4,1,4,1,2,2,2,2,3,1,3,1,2,1,5,2,2,2
%N A330757 Let d(1) < d(2) < ... < d(q) denote the divisors of n; a(n) is the number of elements of the set { d(1)/d(2), d(2)/d(3), ..., d(q-1)/d(q) }.
%C A330757 This sequence is a variant of A060682; here we consider the quotients, there the differences of consecutive divisors.
%C A330757 The sequence is unbounded since a(n!) >= n-1 for any n > 0.
%F A330757 a(n) = 1 iff n is a prime power (A246655).
%e A330757 For n = 42:
%e A330757 - the divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42,
%e A330757 - the corresponding quotients are: 1/2, 2/3, 1/2, 6/7, 1/2, 2/3, 1/2,
%e A330757 - which corresponds to the set { 1/2, 2/3, 6/7 },
%e A330757 - hence a(42) = 3.
%o A330757 (PARI) a(n) = my (d=divisors(n)); #Set(vector(#d-1, k, d[k]/d[k+1]))
%Y A330757 Cf. A060682, A246655.
%K A330757 nonn
%O A330757 1,6
%A A330757 _Rémy Sigrist_, Dec 29 2019