A096736 a(1) = 2; for n>1: a(n) = integer part of x-value when y=0 in (y-tau(n))/(x-1)=(1-tau(n))/(n-1), tau=A000005.

2, 3, 5, 5, 9, 7, 13, 10, 13, 13, 21, 14, 25, 18, 19, 19, 33, 21, 37, 23, 27, 29, 45, 27, 37, 34, 35, 33, 57, 34, 61, 38, 43, 45, 46, 40, 73, 50, 51, 45, 81, 47, 85, 52, 53, 61, 93, 53, 73, 59, 67, 62, 105, 61, 73, 63, 75, 77, 117, 65, 121, 82, 75, 74, 86, 75, 133, 81, 91

Offset

1,1

Comments

a(n) < 2*n; a(n) = 2*n-1 iff n is prime;

let m=A096738(n): a(m)=(m*tau(m)-1)/(tau(m)-1).

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = floor((n*tau(n)-1)/(tau(n)-1)) for n>1, a(1) = 2.

Example

Divisors of n=12: {1,2,3,4,6,12}, A000005(12)=6:
a(12) = floor((12*6-1)/(6-1)) = floor(71/5) = floor(14.2)=14:
+--O
|..| .. div=1
+--+--+
|..|..| ... div=2
+--+--+--+
|..|..|..| .... div=3
+--+--+--+--+
|..|..|..|..| ..... div=4
+--+--+--+--+--+--+
|..|..|..|..|..|..| ....... div=6
+--+--+--+--+--+--+--+--+--+--+--+--O
|..|..|..|..|..|..|..|..|..|..|..|..| ............. div=12
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+X-+--+-
0__1__2__3__4__5__6__7__8__9_10_11_12_13_14_15_16 ....

Mathematica

Join[{2}, Table[Floor[(n*DivisorSigma[0, n] - 1)/(DivisorSigma[0, n] - 1)], {n, 2, 100}]] (* G. C. Greubel, Nov 27 2016 *)

Crossrefs

Cf. A096737.

Sequence in context: A326061 A348203 A158901 * A128188 A318636 A366975

Adjacent sequences: A096733 A096734 A096735 * A096737 A096738 A096739

Keyword

nonn

Author

Reinhard Zumkeller, Jul 06 2004

Status

approved