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

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

Author

Reinhard Zumkeller, May 15 2002

Keywords

• nonn
• easy

Comments

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

Examples

			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
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences computed from exponents in factorization of n.

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.

Programs

Mathematica

a[n_] := FactorInteger[DivisorSigma[0, n]][[1, 1]]; Array[a, 90] (* Jean-François Alcover, Oct 01 2016 *)

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

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

Extensions

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