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Totally multiplicative sequence with a(p) = 2p+1 for prime p.
2

%I #7 May 21 2016 22:34:54

%S 1,5,7,25,11,35,15,125,49,55,23,175,27,75,77,625,35,245,39,275,105,

%T 115,47,875,121,135,343,375,59,385,63,3125,161,175,165,1225,75,195,

%U 189,1375,83,525,87,575,539,235,95,4375,225,605

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

%H G. C. Greubel, <a href="/A166660/b166660.txt">Table of n, a(n) for n = 1..10000</a>

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

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((2*fi[[All, 1]] + 1)^fi[[All, 2]]) ); Table[a[n], {n, 1, 100}](* _G. C. Greubel_, May 21 2016 *)

%K nonn,mult

%O 1,2

%A _Jaroslav Krizek_, Oct 18 2009