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A125096 Expansion of -1 + (phi(q) * phi(q^2) + phi(-q^2) * phi(q^4)) / 2 in powers of q. 1

%I

%S 1,0,2,2,0,0,0,2,3,0,2,4,0,0,0,2,2,0,2,0,0,0,0,4,1,0,4,0,0,0,0,2,4,0,

%T 0,6,0,0,0,0,2,0,2,4,0,0,0,4,1,0,4,0,0,0,0,0,4,0,2,0,0,0,0,2,0,0,2,4,

%U 0,0,0,6,2,0,2,4,0,0,0,0,5,0,2,0,0,0,0,4,2,0,0,0,0,0,0,4,2,0,6,2,0,0,0,0,0

%N Expansion of -1 + (phi(q) * phi(q^2) + phi(-q^2) * phi(q^4)) / 2 in powers of q.

%F a(n) is multiplicative with a(2) = 0, a(2^e) = 2 if e>1, a(p^e) = e+1 if p == 1, 3 (mod 8), a(p^e) = (1+(-1)^e)/2 if p == 5, 7 (mod 8).

%F a(4*n + 2) = a(8*n + 5) = a(8*n + 7) = 0. a(4*n) = 2 * A002325(n). a(8*n + 1) = A112603(n). a(8*n + 3) = A033761(n).

%o (PARI) {a(n) = if( n<1, 0, qfrep([1, 0; 0, 8], n)[n] + qfrep([3, 1; 1, 3], n)[n])}

%Y Cf. A002324, A033761, A112603.

%K nonn,mult

%O 1,3

%A _Michael Somos_, Nov 20 2006

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Last modified August 8 15:35 EDT 2022. Contains 356009 sequences. (Running on oeis4.)