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%I #20 Dec 02 2021 07:32:46
%S 1,0,2,3,3,2,2,3,4,3,3,2,5,4,3,2,5,4,4,3,2,5,5,4,7,5,6,3,2,3,1,4,5,3,
%T 6,3,2,5,6,4,6,2,4,4,4,7,3,4,5,7,5,3,7,6,5,4,6,3,4,7,4,8,4,6,3,3,4,4,
%U 3,3,2,7,9,2,7,1,3,2,7,4,7,3,4,6,7
%N a(1) = 1; a(n+1) is the number of distinct prime divisors of concatenation a(1), a(2), a(3), ..., a(n).
%e a(1) = 1 (given).
%e a(2) = 0 (number of distinct prime divisors of 1).
%e a(3) = 2 (number of distinct prime divisors of 10); etc.
%t l = {1}; s = "1"; Do[k = ToExpression[s]; m = Length[FactorInteger[k]]; AppendTo[l, m]; s = s <> ToString[m], {n, 1, 100}]; Print[l] (* _Ryan Propper_, Oct 10 2005 *)
%o (Python)
%o from sympy import factorint
%o def aupton(terms):
%o alst, astr = [1], "1"
%o for n in range(2, terms+1):
%o an = len(factorint(int(astr)))
%o alst.append(an)
%o astr += str(an)
%o return alst
%o print(aupton(45)) # _Michael S. Branicky_, Dec 02 2021
%Y Cf. A110762, A110763.
%K base,nonn
%O 1,3
%A _Amarnath Murthy_, Aug 11 2005
%E More terms from _Ryan Propper_, Oct 10 2005
%E Definition corrected by _N. J. A. Sloane_, Oct 14 2020 at the suggestion of _David James Sycamore_
%E a(71)-a(85) from _Michael S. Branicky_, Dec 02 2021
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