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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 (list; graph; refs; listen; history; text; internal format)
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_j-th 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}](* Jean-Fran├žois 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

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Last modified December 4 09:05 EST 2016. Contains 278749 sequences.