A071178 Exponent of the largest prime factor of n.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1

Offset

1,4

Comments

a(n) = A067255(n,A001222(n)). - Reinhard Zumkeller, Jun 11 2013

a(n) = the multiplicity of the largest part in the partition having Heinz number n. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 2, 4, 10] we get 2*2*3*7*29 = 2436. Example: a(18) = 2; indeed, the partition having Heinz number 18 = 2*3*3 is [1,2,2]. - Emeric Deutsch, Jun 04 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A124010(n, A001221(n)); A053585(n) = A006530(n)^a(n). [Reinhard Zumkeller, Aug 27 2011]

Maple

with(numtheory): with(padic):
a:= n-> `if`(n=1, 0, ordp(n, max(factorset(n)[]))):
seq(a(n), n=1..120);  # Alois P. Heinz, Jun 04 2015

Mathematica

a[n_] := FactorInteger[n] // Last // Last; Table[a[n], {n, 1, 120}] (* Jean-François Alcover, Jun 12 2015 *)

Prog

(Haskell)
a071178 = last . a124010_row -- Reinhard Zumkeller, Aug 27 2011
(Python)
from sympy import factorint
def A071178(n): return max(factorint(n).items())[1] if n>1 else 0 # Chai Wah Wu, Oct 10 2023

Crossrefs

Cf. A067029, A215366.

Sequence in context: A327503 A051904 A070012 * A366895 A326515 A319864

Adjacent sequences: A071175 A071176 A071177 * A071179 A071180 A071181

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 10 2002

Status

approved