OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
FORMULA
a(n) = Sum_{k=floor(n/2)+1..n} k*c(k), where c is the prime characteristic (A010051). - Wesley Ivan Hurt, Dec 23 2023
a(n) = A063956(n!). - Amiram Eldar, Jul 24 2024
EXAMPLE
Prime divisors of 20! which have exponent 1 (i.e., unitary prime divisors) are {11, 13, 17, 19}, so a(20) = 11 + 13 + 17 + 19= 60. (The sum of all its prime divisors (unitary and non-unitary) is A034387(20).)
MAPLE
a:= n-> add(`if`(i[2]=1, i[1], 0), i=ifactors(n!)[2]):
seq(a(n), n=1..60); # Alois P. Heinz, Jun 24 2018
MATHEMATICA
a[n_] := Select[FactorInteger[n!], #[[2]] == 1&][[All, 1]] // Total;
Array[a, 60] (* Jean-François Alcover, Jan 01 2022 *)
PROG
(PARI) a(n) = my(f=factor(n!)~); sum(i=1, length(f), if (f[2, i]==1, f[1, i])); \\ Harry J. Smith, Sep 04 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Sep 04 2001
STATUS
approved