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 A061395 Let p be the largest prime factor of n; if p is the k-th prime then set a(n) = k; a(1) = 0 by convention. 193
 0, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 3, 1, 7, 2, 8, 3, 4, 5, 9, 2, 3, 6, 2, 4, 10, 3, 11, 1, 5, 7, 4, 2, 12, 8, 6, 3, 13, 4, 14, 5, 3, 9, 15, 2, 4, 3, 7, 6, 16, 2, 5, 4, 8, 10, 17, 3, 18, 11, 4, 1, 6, 5, 19, 7, 9, 4, 20, 2, 21, 12, 3, 8, 5, 6, 22, 3, 2, 13, 23, 4, 7, 14, 10, 5, 24, 3, 6, 9, 11, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Records occur at the primes. - Robert G. Wilson v, Dec 30 2007. For n > 1: length of n-th row in A067255. - Reinhard Zumkeller, Jun 11 2013 a(n) = the largest 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(20) = 3; indeed, the partition having Heinz number 20 = 2*2*5 is [1,1,3]. - Emeric Deutsch, Jun 04 2015 LINKS Álvar Ibeas, Table of n, a(n) for n = 1..100000 (first 1000 terms from Harry J. Smith) FORMULA A000040(a(n)) = A006530(n); a(n) = A049084(A006530(n)). - Reinhard Zumkeller, May 22 2003 A243055(n) = a(n) - A055396(n). - Antti Karttunen, Mar 07 2017 EXAMPLE a(20) = 3 since the largest prime factor of 20 is 5, which is the 3rd prime. MAPLE with(numtheory): a:= n-> `if`(n=1, 0, pi(max(factorset(n)[]))): seq(a(n), n=1..100);  # Alois P. Heinz, Aug 03 2013 MATHEMATICA Insert[Table[PrimePi[FactorInteger[n][[ -1]][]], {n, 2, 120}], 0, 1] (* Stefan Steinerberger, Apr 11 2006 *) f[n_] := PrimePi[ FactorInteger@n][[ -1, 1]]; Array[f, 94] (* Robert G. Wilson v, Dec 30 2007 *) PROG (PARI) { for (n=1, 1000, if (n==1, a=0, f=factor(n)~; p=f[1, length(f)]; a=primepi(p)); write("b061395.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 22 2009 (Haskell) a061395 = a049084 . a006530  -- Reinhard Zumkeller, Jun 11 2013 (Python) from sympy import primepi, primefactors def a(n): return 0 if n==1 else primepi(primefactors(n)[-1]) print [a(n) for n in xrange(1, 101)] # Indranil Ghosh, May 14 2017 CROSSREFS Cf. A006530, A055396, A061394, A133674, A243055. Sequence in context: A108230 A324729 A253558 * A290103 A156061 A225395 Adjacent sequences:  A061392 A061393 A061394 * A061396 A061397 A061398 KEYWORD easy,nice,nonn AUTHOR Henry Bottomley, Apr 30 2001 EXTENSIONS Definition reworded by N. J. A. Sloane, Jul 01 2008 STATUS approved

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Last modified October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)