A179942 Number of times n appears in a 1000 X 1000 multiplication table.

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 7, 4, 8, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4, 4, 8, 2, 12, 4, 6, 4, 4, 4, 12, 2, 6, 6, 9

Offset

1,2

Comments

Identical to A000005(n), the number of divisors of n, for n <= 1000.

As the size of the multiplication table grows, sequences of this kind approach A000005: the number of divisors of n. Any term becomes stable once the size equals or exceeds n. - Robert G. Wilson v, Aug 03 2010

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = 0 for n > 10^6.

Example

a(2)=2 because the number 2 appears in 2 cells in a 1000 X 1000 multiplication table.

Mathematica

nn = 1000; mtab = Flatten[Table[i*j, {i, nn}, {j, nn}]]; Table[Count[mtab, n], {n, 10000}]

Prog

(PARI) a(n)=sumdiv(n, d, d<1001 && n/d<1001) \\ Charles R Greathouse IV, Dec 27 2016

Crossrefs

Cf. A179940, A179941.

Sequence in context: A184395 A329484 A179941 * A000005 A122667 A122668

Adjacent sequences: A179939 A179940 A179941 * A179943 A179944 A179945

Keyword

nonn,fini,less

Author

Dominick Cancilla, Aug 02 2010

Extensions

Observations rephrased as facts by R. J. Mathar, Aug 03 2010

Status

approved