

A055396


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


41



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


REFERENCES

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


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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


CROSSREFS

Cf. sieve of Eratosthenes: A004280, A038179, A055399.
Sequence in context: A087267 A128267 A028920 * A057499 A241919 A064839
Adjacent sequences: A055393 A055394 A055395 * A055397 A055398 A055399


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 15 2000


STATUS

approved



