A195094 G.f.: Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n)^3.

1, 3, 5, 10, 14, 18, 27, 36, 39, 52, 65, 68, 90, 102, 100, 136, 152, 150, 189, 200, 198, 250, 275, 264, 310, 348, 333, 396, 434, 392, 495, 528, 490, 592, 588, 588, 702, 738, 684, 784, 860, 780, 945, 980, 876, 1078, 1127, 1040, 1197, 1220, 1168, 1368, 1430, 1314, 1460, 1560, 1458, 1708

Offset: 1

Author

Paul D. Hanna, Sep 08 2011

Keywords

• nonn

Comments

Compare the g.f. of this sequence to the following identities:

. Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n)^2 = Sum_{n>=1} phi(2*n)*x^n;

. Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n) = Sum_{n>=0} x^(2^n).

Examples

			G.f.: A(x) = x + 3*x^2 + 5*x^3 + 10*x^4 + 14*x^5 + 18*x^6 + 27*x^7 +...
where A(x) = x/(1-x^1)^3 + 0*x^2/(1-x^2)^3 - x^3/(1-x^3)^3 + 0*x^4/(1-x^4)^3 - x^5/(1-x^5)^3 + 0*x^6/(1-x^6)^3 - x^7/(1-x^7)^3 + 0*x^8/(1-x^8)^3 + 0*x^9/(1-x^9)^3 + 0*x^10/(1-x^10)^3 - x^11/(1-x^11)^3 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..8200

Programs

PARI

{a(n)=polcoeff(sum(m=1,n,-moebius(2*m)*x^m/(1-x^m+x*O(x^n))^3),n)}

Formula

a(2^n) = 2^(n-1)*(1 + 2^n) for n>=1.