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%I #12 Sep 20 2020 04:38:00
%S 1,15,24,225,48,360,80,3375,576,720,168,5400,224,1200,1152,50625,360,
%T 8640,440,10800,1920,2520,624,81000,2304,3360,13824,18000,960,17280,
%U 1088,759375,4032,5400,3840,129600,1520,6600,5376,162000,1848,28800
%N Totally multiplicative sequence with a(p) = (p+1)*(p+3) = p^2+4p+3 for prime p.
%H G. C. Greubel, <a href="/A167353/b167353.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = ((p+1)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)+3))^e(k). a(n) = A003959(n) * A166591(n).
%F Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 4*p + 2)) = 1.1854020769112984236586594287311260820805752130814044791625914047437286210... - _Vaclav Kotesovec_, Sep 20 2020
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 11 2016 *)
%Y Cf. A003959, A166591.
%K nonn,mult
%O 1,2
%A _Jaroslav Krizek_, Nov 01 2009
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