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A071187 Smallest prime factor of number of divisors of n; a(1) = 1.

%I A071187 #26 Jan 15 2024 01:47:59
%S A071187 1,2,2,3,2,2,2,2,3,2,2,2,2,2,2,5,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,
%T A071187 2,3,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,7,2,2,2,2,
%U A071187 2,2,2,2,2,2,2,2,2,2,2,2,5,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2
%N A071187 Smallest prime factor of number of divisors of n; a(1) = 1.
%C A071187 a(n) = 2 for nonsquare n. - _David A. Corneth_, Jul 24 2017
%H A071187 Antti Karttunen, <a href="/A071187/b071187.txt">Table of n, a(n) for n = 1..100000</a>
%H A071187 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A071187 a(n) = A020639(A000005(n)).
%F A071187 a(A108951(n)) = A329614(n). - _Antti Karttunen_, Nov 17 2019
%F A071187 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - _Amiram Eldar_, Jan 15 2024
%e A071187 324 = 18^2 = 2^2 * 3^4 has (2+1)*(4+1) = 3 * 5 = 15 divisors, thus a(324) = A020639(15) = 3. - _Antti Karttunen_, Nov 18 2019
%t A071187 a[n_] := FactorInteger[DivisorSigma[0, n]][[1, 1]]; Array[a, 90] (* _Jean-François Alcover_, Oct 01 2016 *)
%o A071187 (PARI) A071187(n) = if(1==n, n, my(f = factor(numdiv(n))); vecmin(f[, 1])); \\ _Antti Karttunen_, Jul 24 2017
%o A071187 (PARI) first(n) = my(v = vector(n, i, 2)); for(i=1,sqrtint(n), v[i^2] = numdiv(i^2)); v
%Y A071187 Cf. A000005, A020639, A071188, A071189, A108951.
%Y A071187 Differs from A329614 for the first time at n=324, where a(324) = 3, while A329614(324) = 5. A329613 gives the positions of differences.
%K A071187 nonn,easy
%O A071187 1,2
%A A071187 _Reinhard Zumkeller_, May 15 2002
%E A071187 Data section extended up to term a(105) by _Antti Karttunen_, Nov 17 2019