1,4

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

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

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

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

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 (since the asymptotic density of A070003 is 0). - Amiram Eldar, Oct 02 2024

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

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

(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

(PARI) a(n) = if(n == 1, 0, my(e = factor(n)[, 2]); e[#e]); \\ Amiram Eldar, Oct 02 2024

Cf. A001221, A001222, A006530, A053585, A067029, A067255, A070003, A124010, A215366.

Sequence in context: A070012 A375034 A373365 * A366895 A326515 A373835

Adjacent sequences: A071175 A071176 A071177 * A071179 A071180 A071181

easy,nonn

Benoit Cloitre, Jun 10 2002

approved