A132802 a(0)=1. a(n) = Sum_{k|n} a(floor(k/2)).

1, 1, 2, 2, 4, 3, 5, 3, 8, 6, 7, 4, 12, 6, 7, 7, 16, 9, 15, 7, 16, 11, 9, 5, 28, 15, 13, 12, 16, 8, 20, 8, 32, 21, 19, 14, 37, 16, 15, 14, 36, 17, 28, 12, 20, 20, 11, 6, 64, 31, 34, 25, 28, 14, 33, 18, 36, 24, 17, 9, 54, 21, 17, 23, 64, 40, 49, 22, 40, 25

Offset

0,3

Comments

a(2^m) = 2^m, for all nonnegative integers m.

a(p * 2^m) = a(p * 2^(m-1)) + 2^(m-1) for odd prime p and m > 0. - David A. Corneth, Jul 30 2015

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Example

The positive divisors of 12 are 1,2,3,4,6,12. These divisors, divided by 2 and rounded down, are 0,1,1,2,3,6. So a(12) = a(0) + a(1) + a(1) + a(2) + a(3) + a(6) = 1 + 1 + 1 + 2 + 2 + 5 = 12.

Mathematica

a = {1}; For[n = 1, n < 70, n++, s = 0; For[j = 1, j < Length[Divisors[n]] + 1, j++, s = s + a[[Floor[Divisors[n][[j]]/2] + 1]]]; AppendTo[a, s]]; a (* Stefan Steinerberger, Nov 20 2007 *)

Prog

(PARI) a(n) = {my(v=vector(n+1)); v[1] = 1; for(i=2, n+1, v[i]=sumdiv(i - 1, X, v[X\2+1])); v} \\ David A. Corneth, Jul 31 2015

Crossrefs

Sequence in context: A145393 A215675 A329439 * A341947 A268353 A204900

Adjacent sequences: A132799 A132800 A132801 * A132803 A132804 A132805

Keyword

nonn

Author

Leroy Quet, Nov 17 2007

Extensions

More terms from Stefan Steinerberger, Nov 20 2007

Status

approved