A106481 An Euler phi transform of 1/(1 - x^2).

0, 1, 1, 3, 3, 7, 5, 13, 9, 19, 13, 29, 17, 41, 23, 49, 31, 65, 37, 83, 45, 95, 55, 117, 63, 137, 75, 155, 87, 183, 95, 213, 111, 233, 127, 257, 139, 293, 157, 317, 173, 357, 185, 399, 205, 423, 227, 469, 243, 511, 263, 543, 287, 595, 305, 635, 329, 671, 357, 729

Offset

0,4

Comments

Apparently A106477 with a leading zero. - R. J. Mathar, Jun 03 2026

Links

Table of n, a(n) for n=0..59.

Formula

a(n) = Sum_{k=0..n} phi(n-k+1)*(k mod 2).

Euler transform of period 7 sequence [3,-2,-1,-1,-2,3,0,...].

a(2n) = A049690(n).

a(2n+1) = A099957(n).

Sum_{k=1..n} a(k) ~ n^3/(2*Pi^2). - Amiram Eldar, Jan 18 2026

Mathematica

With[{r = 2*Range[0, 30]}, Riffle[Accumulate[EulerPhi[r]], Accumulate[EulerPhi[r+1]]]] (* Amiram Eldar, Jan 18 2026 *)

Prog

(PARI) a(n) = sum(k=0, n, if (k%2, eulerphi(n-k+1))); \\ Michel Marcus, Jun 12 2024
(Python)
# uses programs from A002088 and A049690
def A106481(n): return A002088(n+1)-A049690(n+1>>1) if n&1 else A049690(n>>1) # Chai Wah Wu, Aug 04 2024

Crossrefs

Cf. A049690, A099957.

Sequence in context: A070801 A114753 A079316 * A106477 A098043 A324866

Adjacent sequences: A106478 A106479 A106480 * A106482 A106483 A106484

Keyword

easy,nonn

Author

Paul Barry, May 03 2005

Status

approved