A073395 Product of sums of prime factors of n: with and without repetition.
0, 4, 9, 8, 25, 25, 49, 12, 18, 49, 121, 35, 169, 81, 64, 16, 289, 40, 361, 63, 100, 169, 529, 45, 50, 225, 27, 99, 841, 100, 961, 20, 196, 361, 144, 50, 1369, 441, 256, 77, 1681, 144, 1849, 195, 88, 625, 2209, 55, 98, 84, 400, 255, 2809, 55, 256, 117, 484
Offset: 1
Examples
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.
Links
- T. D. Noe, Table of n, a(n) for n = 1..10000
Programs
-
Haskell
a073395 n = a008472 n * a001414 n -- Reinhard Zumkeller, Oct 28 2015 (fixed), Mar 29 2012
-
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 *) -
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
Comments