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A229949
Number of divisors of the n-th positive quarter-square.
1
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
1,2
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
FORMULA
a(n) = A000005(A002620(n+1)).
MATHEMATICA
a[n_] := DivisorSigma[0, Floor[(n+1)^2/4]]; Array[a, 100] (* Amiram Eldar, Dec 03 2023 *)
PROG
(PARI) a(n) = numdiv((n+1)^2\4); \\ Amiram Eldar, Dec 03 2023
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Oct 24 2013
STATUS
approved