A229949 Number of divisors of the n-th positive quarter-square.

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

Offset: 1

Author

Omar E. Pol, Oct 24 2013

Keywords

• nonn
• easy

Comments

Also A048691 and A092517 interleaved.

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.

a(n) has the same parity of n.

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = numdiv((n+1)^2\4); \\ Amiram Eldar, Dec 03 2023

Formula

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