A329614 Smallest prime factor of the number of divisors of A108951(n).

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

Antti Karttunen, Nov 17 2019

Keywords

• nonn

Comments

Differs from A071187 for the first time at n=324, where a(324) = 5, while A071187(324) = 3. The positions of the differences are listed at A329613.

Examples

			324 = 18^2 = 2^2 * 3^4, thus A108951(324) = 2^2 * (2*3)^4 = 2^6 * 3^4 = 5184, which has (6+1)*(4+1) = 7 * 5 = 35 divisors, thus a(324) = A020639(35) = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A020639, A034386, A071187, A108951, A329605, A329608, A329612, A329613.

Programs

Mathematica

Array[FactorInteger[DivisorSigma[0, #]][[1, 1]] &@ Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]] &, 105] (* Michael De Vlieger, Nov 18 2019 *)

PARI

A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A071187(n) = if(1==n, n, my(f = factor(numdiv(n))); vecmin(f[, 1]));
A329614(n) = A071187(A108951(n));

Formula

a(n) = A071187(A108951(n)).

a(n) = A020639(A329605(n)).