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 A055396 Smallest prime dividing n is a(n)-th prime (a(1)=0). 184
 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 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 For n > 1, a(n) gives the number of row where n occurs in arrays A083221 and A246278. - Antti Karttunen, Mar 07 2017 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). FORMULA From Reinhard Zumkeller, May 22 2003: (Start) a(n) = A049084(A020639(n)). A000040(a(n)) = A020639(n); a(n) <= A061395(n). (End) From Antti Karttunen, Mar 07 2017: (Start) A243055(n) = A061395(n) - a(n). a(A276086(n)) = A257993(n). (End) 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 = 0; a[n_] := PrimePi[ FactorInteger[n][[1, 1]] ]; Table[a[n], {n, 1, 96}](* Jean-François 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 (Python) from sympy import primepi, isprime, primefactors def a049084(n): return primepi(n)*(1*isprime(n)) def a(n): return 0 if n==1 else a049084(min(primefactors(n))) # Indranil Ghosh, May 05 2017 CROSSREFS Cf. A004280, A020639, A032742, A038179, A049084, A055399, A061395, A215366, A243055, A257993, A276086. Cf. also A078898, A246277, A250469 and arrays A083221 and A246278. Sequence in context: A289508 A028920 A260738 * A302788 A057499 A241919 Adjacent sequences:  A055393 A055394 A055395 * A055397 A055398 A055399 KEYWORD nonn AUTHOR Henry Bottomley, May 15 2000 STATUS approved

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Last modified September 24 20:13 EDT 2020. Contains 337321 sequences. (Running on oeis4.)