A108728 Number of distinct prime divisors of concatenated even numbers.

1, 2, 3, 2, 5, 3, 2, 3, 6, 5, 3, 4, 6, 4, 5, 4, 3, 5, 4, 7, 6, 5, 8, 3, 7, 4, 4, 8, 5, 7, 4, 4, 8, 5, 7, 6, 4, 8, 8, 7, 5, 3, 7, 4, 6, 10, 11, 5, 4, 10, 6, 5, 6, 5, 5, 4, 9, 4, 8, 9, 6, 5, 8, 4, 12, 5, 4, 8, 10, 5, 9, 7, 6, 8, 8, 5, 10, 5, 9, 7, 5, 5, 8, 3, 11, 6, 6, 7, 9, 10

Offset

1,2

Links

Table of n, a(n) for n=1..90.

Apurva Rai and Michael S. Branicky, Prime Factorizations of OEIS A019520.

Formula

a(n) = A001221(A019520(n)). - Amiram Eldar, Jan 27 2020

Example

2 has 1 distinct prime divisors, so a(1) = 1.
24 has 2 distinct prime divisors, so a(2) = 2.
246 has 3 distinct prime divisors, so a(3) = 3.

Mathematica

a[n_] := PrimeNu @ FromDigits @ Flatten[IntegerDigits /@ (2*Range[n])]; Array[a, 30] (* Amiram Eldar, Jan 27 2020 *)

Crossrefs

Cf. A001221, A019520, A105388 (number of divisors).

Sequence in context: A054494 A306252 A112764 * A331962 A302170 A049805

Adjacent sequences: A108725 A108726 A108727 * A108729 A108730 A108731

Keyword

nonn,base

Author

Parthasarathy Nambi, Jun 21 2005

Extensions

a(43)-a(52) from Amiram Eldar, Jan 27 2020

a(53)-a(54) from Jinyuan Wang, Jun 27 2020

a(55)-a(69) from Apurva Rai and Michael S. Branicky, Aug 16 2020

a(70)-a(71) from Max Alekseyev, Mar 21 2023

a(72)-a(89) from Tyler Busby, Mar 23 2023

a(90) from Tyler Busby, Apr 20 2024

Status

approved