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A300668
a(n) = A000016(2*n).
1
1, 1, 2, 6, 16, 52, 172, 586, 2048, 7286, 26216, 95326, 349536, 1290556, 4793492, 17895736, 67108864, 252645136, 954437292, 3616814566, 13743895360, 52357696956, 199911205052, 764877654106, 2932031008768, 11258999068468, 43303842570872, 166799986203766, 643371375338656, 2484744621997516
OFFSET
0,3
LINKS
FORMULA
a(n) = (1/(4*n)) * Sum_{odd d divides n} phi(d)*4^(n/d) for n > 0.
a(n+1) = A300628(n,0).
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#] * 4^(n/#) &, OddQ[#] &] / (4*n); a[0] = 1; Array[a, 30, 0] (* Amiram Eldar, Oct 04 2023 *)
PROG
(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
CROSSREFS
Cf. A000010 (phi), A000016, A300628.
Sequence in context: A214833 A263593 A003446 * A263594 A263595 A263596
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 10 2018
STATUS
approved