STATUS
reviewed
approved
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Revision History for A080736
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Multiplicative function defined by a(1)=1, a(2)=0, a(2^r) = phi(2^r) (r>1), a(p^r) = phi(p^r) (p odd prime, r>=1), where phi is Euler's function A000010.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
FORMULA
From Amiram Eldar, Nov 02 2023: (Start)
Multiplicative with a(2) = 0, a(2^e) = 2^(e-1) for e >= 2, and a(p^e) = (p-1)*p^(e-1) for an odd prime p.
Dirichlet g.f.: (1 - 2^(1-s) + 1/(2^s-1)) * zeta(s-1) / zeta(s).
Sum_{k=1..n} a(k) ~ (5/(2*Pi^2)) * n^2. (End)
MATHEMATICA
a[n_] := If[Mod[n, 4] == 2, 0, EulerPhi[n]]; Array[a, 100] (* Amiram Eldar, Nov 02 2023 *)
COMMENTS
a(A016825(n)) = 0; a(A000040(n)) = A000040(n) - 1. - Reinhard Zumkeller, Jun 11 2012
FORMULA
a(A016825(n)) = 0; a(A000040(n)) = A000040(n) - 1. - Reinhard Zumkeller, Jun 11 2012
STATUS
approved
editing
LINKS
_Reinhard Zumkeller_, , <a href="/A080736/b080736.txt">Table of n, a(n) for n = 1..10000</a>
LINKS
_Reinhard Zumkeller, _, <a href="/A080736/b080736.txt">Table of n, a(n) for n = 1..10000</a>
STATUS
editing
approved
FORMULA
a(n) = if n mod 4 = 2 then 0 else A000010(n). -~~~~ _Reinhard Zumkeller_, Jun 13 2012
FORMULA
a(n) = if n mod 4 = 2 then 0 else A000010(n). -~~~~
PROG
a080736 n = if n `mod` 4 == 2 then 0 else a000010 n
| even n && odd (div n 2) = 0
| otherwise = product $ map a000010 $ a141809_row n
-- Reinhard Zumkeller, Jun 13 2012, Jun 11 2012
STATUS
approved
editing