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.

A167359 Totally multiplicative sequence with a(p) = (p+2)*(p-3) = p^2-p-6 for prime p.

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%I A167359 #17 Dec 15 2022 06:13:34
%S A167359 1,-4,0,16,14,0,36,-64,0,-56,104,0,150,-144,0,256,266,0,336,224,0,
%T A167359 -416,500,0,196,-600,0,576,806,0,924,-1024,0,-1064,504,0,1326,-1344,0,
%U A167359 -896,1634,0,1800,1664,0,-2000,2156,0,1296,-784,0,2400,2750,0,1456
%N A167359 Totally multiplicative sequence with a(p) = (p+2)*(p-3) = p^2-p-6 for prime p.
%H A167359 G. C. Greubel, <a href="/A167359/b167359.txt">Table of n, a(n) for n = 1..1000</a>
%F A167359 Multiplicative with a(p^e) = ((p+2)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+2)*(p(k)-3))^e(k).
%F A167359 a(3k) = 0 for k >= 1.
%F A167359 a(n) = A166590(n) * A166589(n).
%F A167359 Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 7/p^3 + 6/p^4) = 0.06114270465... . - _Amiram Eldar_, Dec 15 2022
%t A167359 a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 11 2016 *)
%Y A167359 Cf. A166589, A166590.
%K A167359 sign,mult
%O A167359 1,2
%A A167359 _Jaroslav Krizek_, Nov 01 2009