OFFSET
1,2
COMMENTS
Coincides with sigma (A000203) for squarefree n. - Franklin T. Adams-Watters, Jan 31 2016
Every positive integer except 2 occurs in this sequence, but none occur infinitely often. For m > 4, there are n > m with a(n) = m. This implies that every integer greater than 4 occurs in the iterated sequence infinitely often. For example, 5 <- 8 <- 125 <- 113^12 <- .... - Franklin T. Adams-Watters, Jan 31 2016
Sum of the powerfree parts of the divisors of n. - Wesley Ivan Hurt, Jun 13 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p+e. - David W. Wilson, Aug 01 2001
a(n) = Sum_{d|n} A055231(d). - Wesley Ivan Hurt, Jun 13 2021
Sum_{k=1..n} a(k) ~ c * n^2, where c = (Pi^4/72) * Product_{p prime} (1 - 2/p^2 + 2/p^4 - 1/p^5) = 0.5342800948... . - Amiram Eldar, Dec 08 2022
MAPLE
A008473 := proc(n) local e, j; e := ifactors(n)[2]:
mul (e[j][1]+e[j][2], j=1..nops(e)) end:
seq (A008473(n), n=1..80);
# Peter Luschny, Jan 17 2011
MATHEMATICA
Array[Times @@ Total /@ FactorInteger[ # ] &, 80] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 28 2006 *)
PROG
(Haskell)
a008473 n = product $ zipWith (+) (a027748_row n) (a124010_row n)
-- Reinhard Zumkeller, Jul 17 2014
(PARI) a(n)=my(f = factor(n)); for (k=1, #f~, f[k, 1] = f[k, 1] + f[k, 2]; f[k, 2] = 1; ); factorback(f); \\ Michel Marcus, Jan 31 2016
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
EXTENSIONS
More terms from Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 28 2006
STATUS
approved