VOOZH about

URL: https://oeis.org/A062791

⇱ A062791 - OEIS

login
A062791
Moebius transform of A001405 (binomial(n, floor(n/2))).
2
1, 1, 2, 4, 9, 16, 34, 64, 123, 241, 461, 900, 1715, 3396, 6423, 12800, 24309, 48477, 92377, 184500, 352679, 704969, 1352077, 2703168, 5200290, 10398883, 20058174, 40113164, 77558759, 155110827, 300540194, 601067520, 1166802646, 2333581909, 4537567606
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_{d|n} A001405(n/d)*mu(d).
EXAMPLE
For n = 7, binomial(7,3) = 35, A001405(7/d) = {binomial(7,3), binomial(1,0)} = {35, 1}, mu(d) = {1, -1}, the sum is a(7) = 35 - 1 = 34.
MAPLE
with(numtheory):
a:= n-> add(binomial(d, iquo(d, 2))*mobius(n/d), d=divisors(n)):
seq(a(n), n=1..40); # Alois P. Heinz, Jul 09 2017
MATHEMATICA
a[n_] := DivisorSum[n, Binomial[#, Floor[#/2]] * MoebiusMu[n/#] &]; Array[a, 35] (* Amiram Eldar, May 28 2025 *)
PROG
(PARI) a(n) = sumdiv(n, d, binomial(d, d\2) * moebius(n/d)); \\ Amiram Eldar, May 28 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 19 2001
EXTENSIONS
Offset corrected by Eric Rowland, Jul 09 2017
STATUS
approved