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Totally multiplicative sequence with a(p) = 4p+1 for prime p.

2

`%I #8 May 22 2016 12:56:20
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`%S 1,9,13,81,21,117,29,729,169,189,45,1053,53,261,273,6561,69,1521,77,
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`%T 1701,377,405,93,9477,441,477,2197,2349,117,2457,125,59049,585,621,
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`%U 609,13689,149,693,689,15309,165,3393,173,3645,3549,837,189,85293,841,3969
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`%N Totally multiplicative sequence with a(p) = 4p+1 for prime p.
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`%H G. C. Greubel, <a href="/A166662/b166662.txt">Table of n, a(n) for n = 1..10000</a>
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`%F Multiplicative with a(p^e) = (4p+1)^e. If n = Product p(k)^e(k) then a(n) = Product (4*p(k)+1)^e(k).
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`%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((4*fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n], {n, 1, 100}] (* _G. C. Greubel_, May 22 2016 *)
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`%K nonn,mult
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`%O 1,2
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`%A _Jaroslav Krizek_, Oct 18 2009
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