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

1,2

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.

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

Formula

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

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

Example

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.

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 *)

Prog

(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));

Crossrefs

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

Sequence in context: A117183 A352503 A071187 * A134852 A071188 A078545

Adjacent sequences: A329611 A329612 A329613 * A329615 A329616 A329617

Keyword

nonn

Author

Antti Karttunen, Nov 17 2019

Status

approved