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

Author

Parthasarathy Nambi, Jun 21 2005

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

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