OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^e if e <= pi(p) = A000720(p), and 1 otherwise.
a(n) = 1 if and only if n is in A325127.
a(n) = n if and only if n is in A276078.
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{k>=1} (p(k)^(2*(k+1)) + p(k)^(2*k+1) - p(k)^(k+1) - p(k)^k + 1)/(p(k)^(2*k+1) * (p(k)+1)) = 0.76189494803691349595..., where p(k) = prime(k).
MATHEMATICA
f[p_, e_] := p^If[e <= PrimePi[p], e, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^if(f[i, 2] <= primepi(f[i, 1]), f[i, 2], 0)); }
CROSSREFS
KEYWORD
nonn,easy,mult,new
AUTHOR
Amiram Eldar, Jan 11 2025
STATUS
approved