A224247 G.f.: Sum_{n>=1} x^n*(1+x)^d(n), where d(n) is the number of divisors of n (A000005).

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 11, 12, 19, 26, 26, 22, 19, 19, 23, 29, 35, 37, 29, 21, 34, 64, 82, 73, 51, 39, 47, 70, 91, 87, 58, 35, 46, 91, 137, 145, 120, 103, 110, 121, 120, 104, 73, 45, 58, 131, 231, 285, 247, 157, 94, 87, 109, 124, 111, 83, 99, 234, 509

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..5000

Example

G.f.: A(x) = x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 9*x^8 +...
where
A(x) = x*(1+x) + x^2*(1+x)^2 + x^3*(1+x)^2 + x^4*(1+x)^3 + x^5*(1+x)^2 + x^6*(1+x)^4 + x^7*(1+x)^2 + x^8*(1+x)^4 + x^9*(1+x)^3 + x^10*(1+x)^4 + x^11*(1+x)^2 + x^12*(1+x)^6 +...

Prog

(PARI) {a(n)=polcoeff(sum(k=1, n, x^k*(1+x)^sigma(k, 0))+x*O(x^n), n)}
for(n=1, 70, print1(a(n), ", "))

Crossrefs

Sequence in context: A191737 A161659 A089657 * A004727 A102352 A248182

Adjacent sequences: A224244 A224245 A224246 * A224248 A224249 A224250

Keyword

nonn

Author

Paul D. Hanna, Apr 01 2013

Status

approved