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A368468
a(n) is the number of exponentially odd divisors of the n-th exponentially odd number.
2
1, 2, 2, 2, 4, 2, 3, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 6, 4, 3, 2, 8, 2, 4, 4, 4, 4, 2, 4, 4, 6, 2, 8, 2, 4, 2, 4, 2, 6, 4, 6, 4, 4, 2, 2, 4, 4, 8, 2, 4, 8, 2, 2, 4, 4, 8, 2, 4, 2, 4, 4, 4, 6, 2, 4, 4, 4, 4, 8, 2, 2, 8, 2, 6, 8, 4, 2, 2, 8, 4, 2, 8, 4, 4, 4, 12, 4
OFFSET
1,2
LINKS
FORMULA
a(n) = A322483(A268335(n)).
MATHEMATICA
f[p_, e_] := (e + 3)/2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[200], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]
(* or *)
f[p_, e_] := If[OddQ[e], (e + 3)/2, 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 0 &]
PROG
(PARI) lista(kmax) = {my(e, d); for(k = 1, kmax, e = factor(k)[, 2]; d = prod(i = 1, #e, if(e[i]%2, (e[i] + 3)/2, 0)); if(d > 0, print1(d, ", "))); }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Dec 26 2023
STATUS
approved