OFFSET
1,2
COMMENTS
If p^k is a power of a prime, then a(p^k) = p^k.
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n * A008480(n). - Ivan Neretin, May 29 2016
EXAMPLE
The primes that divide 12 are 2 and 3. So a(12) = a(12/2)*2 + a(12/3)*3 = 12*2 + 4*3 = 36.
MATHEMATICA
a = {1}; For[n = 2, n < 100, n++, b = Select[Divisors[n], PrimeQ[ # ] &]; AppendTo[a, Sum[a[[n/b[[j]]]]*b[[j]], {j, 1, Length[b]}]]]; a (* Stefan Steinerberger, Dec 07 2007 *)
Fold[Append[#1, Plus @@ ((p = Select[Divisors[#2], PrimeQ])*#1[[#2/p]])] &, {1}, Range[2, 66]] (* Ivan Neretin, May 29 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 06 2007
EXTENSIONS
More terms from Stefan Steinerberger, Dec 07 2007
STATUS
approved