A064146 - OEIS

%I #22 Mar 02 2022 07:44:07

%S 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,

%T 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,

%U 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

%N Sum of non-unitary prime divisors (A034444, A056169) of central binomial coefficient C(n,floor(n/2)) (A001405). If A001405(n) is squarefree (A046098) then a(n)=0.

%H Alois P. Heinz, <a href="/A064146/b064146.txt">Table of n, a(n) for n = 1..7500</a> (first 1000 terms from Harry J. Smith)

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

%p a:= n-> add(`if`(i[2]>1, i[1], 0), i=ifactors(binomial(n, iquo(n,2)))[2]):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jun 24 2018

%t a[n_] := Sum[If[i[[2]] > 1, i[[1]], 0], {i, FactorInteger[ Binomial[n, Quotient[n, 2]]]}];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Mar 02 2022, after _Alois P. Heinz_ *)

%o (PARI) { for (n=1, 1000, f=factor(binomial(n, n\2))~; a=0; for (i=1, length(f), if (f[2, i]>1, a+=f[1, i])); write("b064146.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 09 2009

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

%K nonn

%O 1,6

%A _Labos Elemer_, Sep 11 2001