

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.


84



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 by 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


EXAMPLE

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


MAPLE

with(numtheory):
a:= n> `if`(n=1, 0, pi(max(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
(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 xrange(1, 101)] # Indranil Ghosh, May 14 2017


CROSSREFS

Cf. A006530, A055396, A061394, A133674, A243055.
Sequence in context: A277564 A108230 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



