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Number of distinct prime factors of prime p concatenated p-1 times.
1

%I #15 Jul 09 2023 09:47:36

%S 1,2,3,5,7,9,10,10,10,11,19,16,14,20,9,12

%N Number of distinct prime factors of prime p concatenated p-1 times.

%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.

%e If p=2, then the number of distinct prime factors of 2 is 1 since 2 is prime.

%e If p=3, then the number of distinct prime factors of 33 is 2.

%e If p=5, then the number of distinct prime factors of 5555 is 3.

%e If p=7, then the number of distinct prime factors of 777777 is 5.

%t f[n_] := Length[ FactorInteger[ FromDigits[ Flatten[ Table[ IntegerDigits[ Prime[n]], {Prime[n] - 1}]] ]]]; Table[ f[n], {n, 10}]

%t dpf[n_]:=Module[{p=Prime[n]},PrimeNu[FromDigits[Flatten[ IntegerDigits/@ Table[p,{p-1}]]]]]; Array[dpf,16] (* _Harvey P. Dale_, Aug 20 2013 *)

%Y Cf. A101081, A102245.

%K nonn,base

%O 1,2

%A _Parthasarathy Nambi_, Feb 18 2005

%E More terms from _Robert G. Wilson v_, Feb 21 2005

%E Corrected and extended by _Harvey P. Dale_, Aug 20 2013