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A167351 Totally multiplicative sequence with a(p) = (p+1)*(p+2) = p^2+3p+2 for prime p. 1

%I

%S 1,12,20,144,42,240,72,1728,400,504,156,2880,210,864,840,20736,342,

%T 4800,420,6048,1440,1872,600,34560,1764,2520,8000,10368,930,10080,

%U 1056,248832,3120,4104,3024,57600,1482,5040,4200,72576,1806,17280,1980,22464

%N Totally multiplicative sequence with a(p) = (p+1)*(p+2) = p^2+3p+2 for prime p.

%H G. C. Greubel, <a href="/A167351/b167351.txt">Table of n, a(n) for n = 1..1000</a>

%F Multiplicative with a(p^e) = ((p+1)*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)+2))^e(k). a(n) = A003959(n) * A166590(n).

%F Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 3*p + 1)) = 1.224476389903759550811745481197762941643093896189832037452375111814242433... - _Vaclav Kotesovec_, Sep 20 2020

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 10 2016 *)

%K nonn,mult

%O 1,2

%A _Jaroslav Krizek_, Nov 01 2009

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Last modified April 19 05:26 EDT 2021. Contains 343105 sequences. (Running on oeis4.)