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A071187
Smallest prime factor of number of divisors of n; a(1) = 1.
7
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, 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, 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
OFFSET
1,2
COMMENTS
a(n) = 2 for nonsquare n. - David A. Corneth, Jul 24 2017
FORMULA
a(n) = A020639(A000005(n)).
a(A108951(n)) = A329614(n). - Antti Karttunen, Nov 17 2019
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Jan 15 2024
EXAMPLE
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
MATHEMATICA
a[n_] := FactorInteger[DivisorSigma[0, n]][[1, 1]]; Array[a, 90] (* Jean-François Alcover, Oct 01 2016 *)
PROG
(PARI) A071187(n) = if(1==n, n, my(f = factor(numdiv(n))); vecmin(f[, 1])); \\ Antti Karttunen, Jul 24 2017
(PARI) first(n) = my(v = vector(n, i, 2)); for(i=1, sqrtint(n), v[i^2] = numdiv(i^2)); v
CROSSREFS
Differs from A329614 for the first time at n=324, where a(324) = 3, while A329614(324) = 5. A329613 gives the positions of differences.
Sequence in context: A145989 A117183 A352503 * A329614 A134852 A071188
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 15 2002
EXTENSIONS
Data section extended up to term a(105) by Antti Karttunen, Nov 17 2019
STATUS
approved