cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A167305 Totally multiplicative sequence with a(p) = 4*(p+2) for prime p.

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%I A167305 #12 Oct 21 2023 05:33:56
%S A167305 1,16,20,256,28,320,36,4096,400,448,52,5120,60,576,560,65536,76,6400,
%T A167305 84,7168,720,832,100,81920,784,960,8000,9216,124,8960,132,1048576,
%U A167305 1040,1216,1008,102400,156,1344,1200,114688,172,11520,180,13312,11200,1600
%N A167305 Totally multiplicative sequence with a(p) = 4*(p+2) for prime p.
%H A167305 G. C. Greubel, <a href="/A167305/b167305.txt">Table of n, a(n) for n = 1..1000</a>
%F A167305 Multiplicative with a(p^e) = (4*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+2))^e(k).
%F A167305 a(n) = A165825(n) * A166590(n) = 4^bigomega(n) * A166590(n) = 4^A001222(n) * A166590(n).
%t A167305 a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 07 2016 *)
%t A167305 f[p_, e_] := (4*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2023 *)
%Y A167305 Cf. A001222, A165825, A166590.
%K A167305 nonn,easy,mult
%O A167305 1,2
%A A167305 _Jaroslav Krizek_, Nov 01 2009