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A071178 Exponent of the largest prime factor of n. 22

%I

%S 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,

%T 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,

%U 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

%N Exponent of the largest prime factor of n.

%C a(n) = A067255(n,A001222(n)). - _Reinhard Zumkeller_, Jun 11 2013

%C 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

%H Reinhard Zumkeller, <a href="/A071178/b071178.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A124010(n, A001221(n)); A053585(n) = A006530(n)^a(n). [_Reinhard Zumkeller_, Aug 27 2011]

%p with(numtheory): with(padic):

%p a:= n-> `if`(n=1, 0, ordp(n, max(factorset(n)[]))):

%p seq(a(n), n=1..120); # _Alois P. Heinz_, Jun 04 2015

%t a[n_] := FactorInteger[n] // Last // Last; Table[a[n], {n, 1, 120}] (* _Jean-Fran├žois Alcover_, Jun 12 2015 *)

%o (Haskell)

%o a071178 = last . a124010_row -- _Reinhard Zumkeller_, Aug 27 2011

%Y Cf. A067029, A215366.

%K easy,nonn

%O 1,4

%A _Benoit Cloitre_, Jun 10 2002

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Last modified December 12 14:47 EST 2017. Contains 295939 sequences.