OFFSET
1,2
FORMULA
a(n) = n * A055457(n).
If n == 0 (mod 5), a(n) = n + 5 * a(n/5) otherwise a(n) = n.
From Amiram Eldar, Jul 14 2023: (Start)
Multiplicative with a(5^e) = (e+1)*5^e and a(p^e) = p*e if p != 5.
Dirichlet g.f.: (5^s/(5^s-5)) * zeta(s-1).
Sum_{k=1..n} a(k) ~ (5/8)*n^2. (End)
MATHEMATICA
a[n_] := n * (IntegerExponent[n, 5] + 1); Array[a, 100] (* Amiram Eldar, Jul 14 2023 *)
PROG
(PARI) a(n) = n*(valuation(n, 5)+1);
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Seiichi Manyama, Jul 14 2023
STATUS
approved