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Number of distinct prime divisors of concatenated even numbers.
3

%I #52 Apr 21 2024 10:01:53

%S 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,

%T 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,

%U 4,8,10,5,9,7,6,8,8,5,10,5,9,7,5,5,8,3,11,6,6,7,9,10

%N Number of distinct prime divisors of concatenated even numbers.

%H Apurva Rai and Michael S. Branicky, <a href="/A108728/a108728.txt">Prime Factorizations of OEIS A019520</a>.

%F a(n) = A001221(A019520(n)). - _Amiram Eldar_, Jan 27 2020

%e 2 has 1 distinct prime divisors, so a(1) = 1.

%e 24 has 2 distinct prime divisors, so a(2) = 2.

%e 246 has 3 distinct prime divisors, so a(3) = 3.

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

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

%K nonn,base

%O 1,2

%A _Parthasarathy Nambi_, Jun 21 2005

%E a(43)-a(52) from _Amiram Eldar_, Jan 27 2020

%E a(53)-a(54) from _Jinyuan Wang_, Jun 27 2020

%E a(55)-a(69) from _Apurva Rai_ and _Michael S. Branicky_, Aug 16 2020

%E a(70)-a(71) from _Max Alekseyev_, Mar 21 2023

%E a(72)-a(89) from _Tyler Busby_, Mar 23 2023

%E a(90) from _Tyler Busby_, Apr 20 2024