cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A167339 Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.

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%I A167339 #17 Dec 15 2022 06:14:43
%S A167339 1,0,3,0,15,0,35,0,9,0,99,0,143,0,45,0,255,0,323,0,105,0,483,0,225,0,
%T A167339 27,0,783,0,899,0,297,0,525,0,1295,0,429,0,1599,0,1763,0,135,0,2115,0,
%U A167339 1225,0
%N A167339 Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.
%H A167339 G. C. Greubel, <a href="/A167339/b167339.txt">Table of n, a(n) for n = 1..1000</a>
%F A167339 Multiplicative with a(p^e) = (p*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-2))^e(k).
%F A167339 a(2k) = 0 for k >= 1.
%F A167339 a(n) = n * A166586(n).
%F A167339 Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 2/p^3) = 0.1016391193... . - _Amiram Eldar_, Dec 15 2022
%t A167339 a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* _G. C. Greubel_, Jun 08 2016 *)
%Y A167339 Cf. A166586.
%K A167339 nonn,mult
%O A167339 1,3
%A A167339 _Jaroslav Krizek_, Nov 01 2009