

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.


297



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

Records occur at the primes.  Robert G. Wilson v, Dec 30 2007.
For n > 1: length of nth row in A067255.  Reinhard Zumkeller, Jun 11 2013
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

Álvar Ibeas, Table of n, a(n) for n = 1..100000 (first 1000 terms from Harry J. Smith)
Index entries for sequences computed from indices in prime factorization


FORMULA

A000040(a(n)) = A006530(n); a(n) = A049084(A006530(n)).  Reinhard Zumkeller, May 22 2003
A243055(n) = a(n)  A055396(n).  Antti Karttunen, Mar 07 2017
a(n) = A000720(A006530(n)).  Alois P. Heinz, Mar 05 2020


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)[])):
seq(a(n), n=1..100); # Alois P. Heinz, Aug 03 2013


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)
a061395 = a049084 . a006530  Reinhard Zumkeller, Jun 11 2013
(Python)
from sympy import primepi, primefactors
def a(n): return 0 if n==1 else primepi(primefactors(n)[1])
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, May 14 2017


CROSSREFS

Cf. A000720, A006530, A055396, A061394, A133674, A243055.
Sequence in context: A324729 A355532 A253558 * A290103 A156061 A225395
Adjacent sequences: A061392 A061393 A061394 * A061396 A061397 A061398


KEYWORD

easy,nice,nonn


AUTHOR

Henry Bottomley, Apr 30 2001


EXTENSIONS

Definition reworded by N. J. A. Sloane, Jul 01 2008


STATUS

approved



