A064146 Sum of non-unitary prime divisors of binomial(n,floor(n/2)).

0, 0, 0, 0, 0, 2, 0, 0, 3, 5, 0, 2, 2, 2, 3, 3, 0, 2, 0, 2, 2, 2, 0, 2, 7, 7, 10, 10, 5, 5, 3, 3, 3, 5, 5, 7, 7, 7, 3, 5, 2, 2, 2, 2, 10, 10, 8, 10, 12, 12, 12, 12, 9, 9, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 7, 9, 7, 9, 5, 5, 0, 2, 2, 2, 7, 7, 14, 14, 7, 9, 12, 12, 5, 5, 10, 10, 10, 10, 5, 5, 12, 12, 12

Offset: 1

Author

Labos Elemer, Sep 11 2001

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..7500 (first 1000 terms from Harry J. Smith)

Crossrefs

Cf. A008472, A001405, A063958, A034444, A056169, A046098, A048243.

Programs

Maple

a:= n-> add(`if`(i[2]>1, i[1], 0), i=ifactors(binomial(n, iquo(n,2)))[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 24 2018

Mathematica

a[n_] := Sum[If[i[[2]] > 1, i[[1]], 0], {i, FactorInteger[ Binomial[n, Quotient[n, 2]]]}];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 02 2022, after Alois P. Heinz *)

PARI

a(n) = { my(f=factor(binomial(n, n\2))); sum(i=1, #f~, if (f[i, 2]>1, f[i,1])) } \\ Harry J. Smith, Sep 09 2009

Formula

a(n) = A063958(A001405(n)).