A062791 Moebius transform of A001405 (binomial(n, floor(n/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
Keywords
Examples
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.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
Programs
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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
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Mathematica
a[n_] := DivisorSum[n, Binomial[#, Floor[#/2]] * MoebiusMu[n/#] &]; Array[a, 35] (* Amiram Eldar, May 28 2025 *)
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PARI
a(n) = sumdiv(n, d, binomial(d, d\2) * moebius(n/d)); \\ Amiram Eldar, May 28 2025
Formula
a(n) = Sum_{d|n} A001405(n/d)*mu(d).
Extensions
Offset corrected by Eric Rowland, Jul 09 2017