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Number of divisors of the n-th positive quarter-square.
1

%I #19 Dec 03 2023 05:01:59

%S 1,2,3,4,3,6,5,6,3,8,9,8,3,8,7,12,5,12,9,8,3,12,15,12,3,8,9,16,9,20,9,

%T 10,3,12,15,12,3,12,15,24,9,16,9,8,3,16,21,24,5,12,9,16,7,24,15,12,3,

%U 16,27,16,3,12,11,24,9,16,9,16,9,36,25,18,3,8

%N Number of divisors of the n-th positive quarter-square.

%C Also A048691 and A092517 interleaved.

%C The first bisection gives A048691, the number of divisors of the squares. The second bisection gives A092517, the number of divisors of the oblong numbers.

%C a(n) has the same parity of n.

%H Amiram Eldar, <a href="/A229949/b229949.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(A002620(n+1)).

%t a[n_] := DivisorSigma[0, Floor[(n+1)^2/4]]; Array[a, 100] (* _Amiram Eldar_, Dec 03 2023 *)

%o (PARI) a(n) = numdiv((n+1)^2\4); \\ _Amiram Eldar_, Dec 03 2023

%Y Cf. A000005, A000290, A002378, A002620, A048691, A092517, A220492.

%K nonn,easy

%O 1,2

%A _Omar E. Pol_, Oct 24 2013