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.

A167334 Totally multiplicative sequence with a(p) = 2*(2p+1) = 4p+2 for prime p.

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%I A167334 #12 Oct 19 2023 02:16:38
%S A167334 1,10,14,100,22,140,30,1000,196,220,46,1400,54,300,308,10000,70,1960,
%T A167334 78,2200,420,460,94,14000,484,540,2744,3000,118,3080,126,100000,644,
%U A167334 700,660,19600,150,780,756,22000,166,4200,174,4600,4312,940,190,140000,900
%N A167334 Totally multiplicative sequence with a(p) = 2*(2p+1) = 4p+2 for prime p.
%H A167334 G. C. Greubel, <a href="/A167334/b167334.txt">Table of n, a(n) for n = 1..1000</a>
%F A167334 Multiplicative with a(p^e) = (2*(2p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(2*p(k)+1))^e(k).
%F A167334 a(n) = A061142(n) * A166660(n) = 2^bigomega(n) * A166660(n) = 2^A001222(n) * A166660(n).
%t A167334 a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((2*fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 06 2016 *)
%t A167334 f[p_, e_] := (4*p+2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)
%Y A167334 Cf. A001222, A061142, A166660.
%K A167334 nonn,easy,mult
%O A167334 1,2
%A A167334 _Jaroslav Krizek_, Nov 01 2009