A053640 Number of divisors of highly composite odd numbers (A053624).

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 24, 32, 36, 40, 48, 54, 64, 72, 80, 96, 108, 120, 128, 144, 160, 192, 216, 240, 256, 288, 320, 384, 432, 480, 512, 576, 640, 720, 768, 864, 960, 1024, 1152, 1280, 1440, 1536, 1728, 1920, 2048, 2304, 2560, 2880, 3072, 3456

Offset

1,2

Comments

a(n) is the number of divisors of the odd parts of A340506(n); see also comments in A250071. - Hartmut F. W. Hoft, Mar 29 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..363 (terms 1..170 from Ray Chandler)

Formula

a(n) = A000005(A053624(n)).

Example

a(15) = 6 since A053624(6) = 45 has the 6 divisors 1, 3, 5, 9, 15, 45. - Hartmut F. W. Hoft, Mar 29 2022

Mathematica

a053640[n_] := Module[{recL={1}, q, d}, For[q=1, q<=n, q+=2, d=Length[Divisors[q]]; If[Last[recL]<d, AppendTo[recL , d]]]; recL]
a053640[150000000] (* Hartmut F. W. Hoft, Mar 29 2022 *)

Crossrefs

Cf. A000005, A053624.

Cf. A237593, A237048, A237270, A250071, A340506.

Sequence in context: A227731 A067947 A279542 * A344470 A296991 A097755

Adjacent sequences: A053637 A053638 A053639 * A053641 A053642 A053643

Keyword

nonn

Author

Stefano Lanfranco (lastefano(AT)yahoo.it), Mar 22 2000

Extensions

Extended by Ray Chandler, Jan 12 2012

Status

approved