A342007 Multiplicative with a(p^e) = p^floor(e/p).

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (p-1)/(p^p-p)) = 1.6270951877598772517... . - Amiram Eldar, Nov 07 2022

Mathematica

Array[Times @@ Map[#1^Floor[#2/#1] & @@ # &, FactorInteger[#]] &, 105] (* Michael De Vlieger, Mar 12 2021 *)

Prog

(PARI) A342007(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = floor(f[k, 2]/f[k, 1])); factorback(f); };

Crossrefs

Cf. A327936, A327938, A327939, A341997, A342017 [= a(A276086(n))].

Sequence in context: A340853 A277872 A161100 * A341997 A053543 A161099

Adjacent sequences: A342004 A342005 A342006 * A342008 A342009 A342010

Keyword

nonn,mult

Author

Antti Karttunen, Mar 04 2021

Status

approved