OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = 1 + Sum_{k=0..floor(log_2(e))} p^(2^k).
Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} ((1-1/p)*(1 + Sum_{k>=1} (Sum_{j=0..floor(log_2(k))} p^(2^j)/p^(2*k)))) = 0.7176001667... . - Amiram Eldar, Nov 19 2022
MATHEMATICA
f[p_, e_] := 1 + Sum[p^(2^k), {k, 0, Floor[Log2[e]]}]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(k = 0, logint(f[i, 2], 2), f[i, 1]^(2^k))); } \\ Amiram Eldar, Nov 19 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, May 10 2022
STATUS
approved