OFFSET
1,2
COMMENTS
First differs from A365298 at n = 64.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^s(e), s(e) = min{k >= e, k is evil} - e.
a(n) = A367934(n)/n.
a(n) >= 1, with equality if and only if n is an exponentially evil number (A262675).
Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = Product_{p prime} f(1/p) = 0.623746285..., where f(x) = (1-x) * (1 + Sum_{k>=1} (x^(3*k-s(k))), and s(k) is defined above.
MATHEMATICA
f[p_, e_] := Module[{k = e}, While[! EvenQ[DigitCount[k, 2 , 1]], k++]; p^(k-e)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(e) = {my(k = e); while(hammingweight(k)%2, k++); k - e; };
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, Dec 05 2023
STATUS
approved