OFFSET
1,2
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
a(15) = (3+5)*(3+5) = 8*8 = 64 (n squarefree); a(16) = (2)*(2+2+2+2) = 2*8 = 16 (n prime-power); a(17) = (17)*(17) = 289 (n prime); a(18) = (2+3)*(2+3+3) = 5*8 = 40.
MATHEMATICA
a[n_] := With[{fi = FactorInteger[n]}, Plus @@ fi[[All, 1]]*Plus @@ Apply[Times, fi, 1]]; a[1]=0; Table[a[n], {n, 1, 57}] (* Jean-François Alcover, Jul 19 2012 *)
PROG
(Haskell)
a073395 n = a008472 n * a001414 n
-- Reinhard Zumkeller, Oct 28 2015 (fixed), Mar 29 2012
(Python)
from sympy import primefactors, factorint
def a001414(n):
f=factorint(n)
return sum([i*f[i] for i in f])
def a(n): return 0 if n==1 else sum(primefactors(n))*a001414(n)
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 23 2017
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Reinhard Zumkeller, Jul 30 2002
STATUS
approved