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A295658
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Multiplicative with a(p^e) = p^max(0,(floor(e/2)-1)).
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3
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,16
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COMMENTS
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(3)/zeta(6) = 1.181564... (A157289). - Amiram Eldar, Nov 30 2022
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EXAMPLE
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For n = 64 = 2^6, a(64) = 2^(floor(6/2)-1) = 2^2 = 4.
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MATHEMATICA
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f[p_, e_] := p^Max[0, Floor[e/2-1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 30 2022 *)
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PROG
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(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^max(0, floor(f[i, 2]/2-1))); } \\ Amiram Eldar, Nov 30 2022
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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