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A365708 a(n) for n >= 2 is the smallest term of A008578 m dividing n such that n/m is not a square, a(1) = 2.

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%I A365708 #24 Jan 01 2024 11:55:17
%S A365708 2,1,1,2,1,1,1,1,3,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,
%T A365708 1,2,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,
%U A365708 1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
%N A365708 a(n) for n >= 2 is the smallest term of A008578 m dividing n such that n/m is not a square, a(1) = 2.
%C A365708 In other words, a(n) is the least prime divisor of n for n = m^2, (m > 1), otherwise a(n) = 1. (Every term is 1 or a prime.) Compare with A007913.
%H A365708 Michael De Vlieger, <a href="/A365708/b365708.txt">Table of n, a(n) for n = 1..10000</a>
%e A365708 a(1) = 2, since 2 is the smallest m such that 1/m is not a square.
%e A365708 a(2) = 1, since 2/1 = 2 is not a square (likewise for all primes p, a(p) = 1).
%e A365708 a(4) = 2, since 4/1 = 4, a square, but 4/2 = 2, not a square, and so on.
%e A365708 If n is a square with lpf(n) = p, then a(n) = p, the least m such that n/m is not a square.
%t A365708 {2}~Join~Table[SelectFirst[Divisors[n], ! IntegerQ@ Sqrt[n/#] &], {n, 2, 120}] (* _Michael De Vlieger_, Sep 17 2023 *)
%o A365708 (PARI) a(n) = fordiv(n, d, if (!issquare(n/d), return(d))); n+1; \\ _Michel Marcus_, Sep 17 2023
%Y A365708 Cf. A007913, A008578, A020639.
%K A365708 nonn
%O A365708 1,1
%A A365708 _David James Sycamore_, Sep 16 2023