A110764 - OEIS

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A110764

a(1) = 1; a(n+1) is the number of distinct prime divisors of concatenation a(1), a(2), a(3), ..., a(n).

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, 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, 3, 3, 2, 7, 9, 2, 7, 1, 3, 2, 7, 4, 7, 3, 4, 6, 7

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..85.

EXAMPLE

a(1) = 1 (given).

a(2) = 0 (number of distinct prime divisors of 1).

a(3) = 2 (number of distinct prime divisors of 10); etc.

MATHEMATICA

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 *)

PROG

(Python)

from sympy import factorint

def aupton(terms):

alst, astr = [1], "1"

for n in range(2, terms+1):

an = len(factorint(int(astr)))

alst.append(an)

astr += str(an)

return alst

print(aupton(45)) # Michael S. Branicky, Dec 02 2021

CROSSREFS