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A372504
Multiplicative with a(p^e) = e if e is a power of 2, and 0 otherwise.
1
1, 1, 1, 2, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 1, 1, 0, 1, 1, 1, 4, 1, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 1, 2, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1
OFFSET
1,4
LINKS
FORMULA
Multiplicative with a(p^e) = A048298(e) = A209229(e) * e.
a(n) = A355823(n) * A005361(n).
a(A138302(n)) = A005361(A138302(n)) = A368473(n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} f(1/p) = 1.31285540951965780409..., where f(x) = (1-x) * (1 + Sum_{k>=0} 2^k * x^(2^k)).
MATHEMATICA
f[p_, e_] := If[e == 2^IntegerExponent[e, 2], e, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> if(x == 1 << valuation(x, 2), x, 0), factor(n)[, 2]));
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, May 04 2024
STATUS
approved