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%I #10 Sep 20 2020 04:33:21
%S 1,9,16,81,36,144,64,729,256,324,144,1296,196,576,576,6561,324,2304,
%T 400,2916,1024,1296,576,11664,1296,1764,4096,5184,900,5184,1024,59049,
%U 2304,2916,2304,20736,1444,3600,3136,26244,1764,9216,1936,11664,9216,5184
%N Totally multiplicative sequence with a(p) = (p+1)^2 = p^2+2p+1 for prime p.
%H G. C. Greubel, <a href="/A167349/b167349.txt">Table of n, a(n) for n = 1..1000</a>
%F Multiplicative with a(p^e) = ((p+1)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)^2)^e(k). a(n) = A003959(n)^2.
%F Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p*(p+2))) = 1.288853271279060013237007191320577437103236294043770723089390440619086825... - _Vaclav Kotesovec_, Sep 20 2020
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]^2, {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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