

A061395


Let p be the largest prime factor of n; if p is the kth prime then set a(n) = k; a(1) = 0 by convention.


355



0, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 3, 1, 7, 2, 8, 3, 4, 5, 9, 2, 3, 6, 2, 4, 10, 3, 11, 1, 5, 7, 4, 2, 12, 8, 6, 3, 13, 4, 14, 5, 3, 9, 15, 2, 4, 3, 7, 6, 16, 2, 5, 4, 8, 10, 17, 3, 18, 11, 4, 1, 6, 5, 19, 7, 9, 4, 20, 2, 21, 12, 3, 8, 5, 6, 22, 3, 2, 13, 23, 4, 7, 14, 10, 5, 24, 3, 6, 9, 11, 15
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OFFSET

1,3


COMMENTS

a(n) = the largest part of the partition having Heinz number n. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_jth 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(20) = 3; indeed, the partition having Heinz number 20 = 2*2*5 is [1,1,3].  Emeric Deutsch, Jun 04 2015


LINKS



FORMULA



EXAMPLE

a(20) = 3 since the largest prime factor of 20 is 5, which is the 3rd prime.


MAPLE

with(numtheory):
a:= n> pi(max(1, factorset(n)[])):


MATHEMATICA

Insert[Table[PrimePi[FactorInteger[n][[ 1]][[1]]], {n, 2, 120}], 0, 1] (* Stefan Steinerberger, Apr 11 2006 *)
f[n_] := PrimePi[ FactorInteger@n][[ 1, 1]]; Array[f, 94] (* Robert G. Wilson v, Dec 30 2007 *)


PROG

(PARI) { for (n=1, 1000, if (n==1, a=0, f=factor(n)~; p=f[1, length(f)]; a=primepi(p)); write("b061395.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 22 2009
(PARI) a(n) = if (n==1, 0, primepi(vecmax(factor(n)[, 1]))); \\ Michel Marcus, Nov 14 2022
(Haskell)
(Python)
from sympy import primepi, primefactors
def a(n): return 0 if n==1 else primepi(primefactors(n)[1])


CROSSREFS



KEYWORD

easy,nice,nonn


AUTHOR



EXTENSIONS



STATUS

approved



