login
A106481
An Euler phi transform of 1/(1 - x^2).
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
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).
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
Sequence in context: A070801 A114753 A079316 * A106477 A098043 A324866
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 03 2005
STATUS
approved