

A055396


Smallest prime dividing n is a(n)th prime (a(1)=0).


87



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

1,3


COMMENTS

A000040(a(n)) = A020639(n); a(n) <= A061395(n).  Reinhard Zumkeller, May 22 2003
Grundy numbers of the game in which you decrease n by a number prime to n, and the game ends when 1 is reached.  Eric M. Schmidt, Jul 21 2013
a(n) = the smallest 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(21) = 2; indeed, the partition having Heinz number 21 = 3*7 is [2,4].  Emeric Deutsch, Jun 04 2015
a(n) is the number of numbers whose largest proper divisor is n, i.e., for n>1, number of occurrences of n in A032742.  Stanislav Sykora, Nov 04 2016


REFERENCES

John H. Conway, On Numbers and Games, 2nd Edition, p. 129.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Wikipedia, Nimber (explains the term Grundy number).
Index entries for sequences generated by sieves


FORMULA

a(n) = A049084(A020639(n)).  Reinhard Zumkeller, May 22 2003


EXAMPLE

a(15) = 2 because 15=3*5, 3<5 and 3 is the 2nd prime.


MAPLE

with(numtheory):
a:= n> `if`(n=1, 0, pi(min(factorset(n)[]))):
seq(a(n), n=1..100); # Alois P. Heinz, Aug 03 2013


MATHEMATICA

a[1] = 0; a[n_] := PrimePi[ FactorInteger[n][[1, 1]] ]; Table[a[n], {n, 1, 96}](* JeanFrançois Alcover, Jun 11 2012 *)


PROG

(Haskell)
a055396 = a049084 . a020639  Reinhard Zumkeller, Apr 05 2012
(PARI) a(n)=if(n==1, 0, primepi(factor(n)[1, 1])) \\ Charles R Greathouse IV, Apr 23 2015


CROSSREFS

Cf. sieve of Eratosthenes: A004280, A038179, A055399, A215366.
Cf. A032742.
Sequence in context: A128267 A028920 A260738 * A057499 A241919 A064839
Adjacent sequences: A055393 A055394 A055395 * A055397 A055398 A055399


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 15 2000


STATUS

approved



