A064142 Sum of all distinct primes dividing central binomial coefficient C(n, floor(n/2)).

0, 2, 3, 5, 7, 7, 12, 14, 12, 12, 23, 23, 29, 29, 32, 34, 48, 48, 62, 62, 61, 61, 81, 81, 73, 73, 69, 69, 98, 98, 127, 129, 123, 123, 130, 130, 148, 148, 161, 161, 195, 195, 227, 227, 204, 204, 251, 251, 253, 253, 257, 257, 307, 307, 323, 323, 316, 316, 367, 367

Offset

1,2

Links

Harry J. Smith and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Smith)

Formula

a(n) = A008472(A001405(n)).

k1 + o(1) < a(n)/(n^2/log n) < k2 + o(1) for k1 = 3/8 and k2 = 1/2. - Charles R Greathouse IV, Jan 26 2023

Mathematica

sop[n_] := If[n<2, 0, Total[First /@ FactorInteger[n]]]; Table[ sop[ Binomial[n, Floor[n/2]]], {n, 60}] (* Giovanni Resta, Jun 22 2018 *)

Prog

(PARI) sopf(n)= my(f, s=0); f=factor(n); for(i=1, matsize(f)[1], s+=f[i, 1]); return(s)
a(n)=sopf(binomial(n, n\2)); \\ Harry J. Smith, Sep 08 2009
(PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
a(n)=my(s); forprime(p=2, n, my(t=valp(n, p)-valp(n\2, p)-valp(n-n\2, p)); if(t, s+=p)); s \\ Charles R Greathouse IV, Jan 26 2023

Crossrefs

Cf. A008472, A001405.

Sequence in context: A060308 A224911 A270176 * A067792 A119317 A198424

Adjacent sequences: A064139 A064140 A064141 * A064143 A064144 A064145

Keyword

nonn

Author

Labos Elemer, Sep 11 2001

Status

approved