

A055396


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


60



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
Denote by B(n) the partition obtained by taking the prime decomposition of the positive integer n>=2 and replacing each prime factor p by its index i (i.e. ith prime = p); also B(1) = the empty partition. B is a bijection between the positive integers and the set of all partitions. For example, B(350) = B(2*5^2*7) = [1,3,3,4]. In the Maple program the subprogram B yields B(n). a(n) is the smallest part in B(n). Emeric Deutsch, May 09 2015


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
(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.
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



