OFFSET
1,2
COMMENTS
First differs from A050985 at n = 32.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n/A366906(n).
Multiplicative with a(p^e) = p^(e-s(e)), where s(e) = max({k=1..e, k evil}).
a(n) >= 1, with equality if and only if n is an exponentially evil number (A262675).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} f(1/p) = 0.84485885044273919581..., where f(x) = (1-x)*(1+Sum_{k>=1} x^(k+s(k))), s(k) is defined above for k >= 1, and s(0) = 0.
MATHEMATICA
maxEvil[e_] := Module[{k = e}, While[OddQ[DigitCount[k, 2, 1]], k--]; k]; f[p_, e_] := p^(e - maxEvil[e]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(n) = {my(k = n); while(hammingweight(k)%2, k--); n-k; }
a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }
CROSSREFS
KEYWORD
nonn,easy,mult,base
AUTHOR
Amiram Eldar, Nov 27 2023
STATUS
approved