login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A167312 Totally multiplicative sequence with a(p) = 2*(p-3) for prime p. 1

%I #12 Oct 21 2023 05:33:53

%S 1,-2,0,4,4,0,8,-8,0,-8,16,0,20,-16,0,16,28,0,32,16,0,-32,40,0,16,-40,

%T 0,32,52,0,56,-32,0,-56,32,0,68,-64,0,-32,76,0,80,64,0,-80,88,0,64,

%U -32,0,80,100,0,64,-64,0,-104,112,0,116,-112,0,64,80,0,128,112

%N Totally multiplicative sequence with a(p) = 2*(p-3) for prime p.

%H G. C. Greubel, <a href="/A167312/b167312.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = (2*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)-3))^e(k).

%F a(3k) = 0 for k >= 1.

%F a(n) = A061142(n) * A166589(n) = 2^bigomega(n) * A166589(n) = 2^A001222(n) * A166589(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 08 2016 *)

%t f[p_, e_] := (2*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2023 *)

%Y Cf. A001222, A061142, A166589.

%K sign,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)