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.

A300668 a(n) = A000016(2*n).

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%I A300668 #30 Oct 04 2023 03:55:59
%S A300668 1,1,2,6,16,52,172,586,2048,7286,26216,95326,349536,1290556,4793492,
%T A300668 17895736,67108864,252645136,954437292,3616814566,13743895360,
%U A300668 52357696956,199911205052,764877654106,2932031008768,11258999068468,43303842570872,166799986203766,643371375338656,2484744621997516
%N A300668 a(n) = A000016(2*n).
%H A300668 Seiichi Manyama, <a href="/A300668/b300668.txt">Table of n, a(n) for n = 0..1667</a>
%F A300668 a(n) = (1/(4*n)) * Sum_{odd d divides n} phi(d)*4^(n/d) for n > 0.
%F A300668 a(n+1) = A300628(n,0).
%t A300668 a[n_] := DivisorSum[n, EulerPhi[#] * 4^(n/#) &, OddQ[#] &] / (4*n); a[0] = 1; Array[a, 30, 0] (* _Amiram Eldar_, Oct 04 2023 *)
%o A300668 (PARI) a(n) = if (n==0, 1, sumdiv(n, d, if (d % 2, eulerphi(d)*4^(n/d)))/(4*n));  \\ _Michel Marcus_, Mar 11 2018
%Y A300668 Cf. A000010 (phi), A000016, A300628.
%K A300668 nonn
%O A300668 0,3
%A A300668 _Seiichi Manyama_, Mar 10 2018