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

Author

Paul Barry, May 03 2005

Keywords

• easy
• nonn

Crossrefs

Cf. A049690, A099957.

Programs

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

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).