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A071187 Smallest prime factor of number of divisors of n. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = 2 for nonsquare n. - David A. Corneth, Jul 24 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = A020639(A000005(n)).

a(A108951(n)) = A329614(n). - Antti Karttunen, Nov 17 2019

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

Cf. A000005, A020639, A071188, A071189, A108951.

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: A064569 A145989 A117183 * A329614 A134852 A071188

Adjacent sequences:  A071184 A071185 A071186 * A071188 A071189 A071190

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 15 2002

EXTENSIONS

Data section extended up to term a(105) by Antti Karttunen, Nov 17 2019

STATUS

approved

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)