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 A078897 Number of times the greatest prime factor of n is a factor in all numbers <=n; a(1)=1. 4
 1, 1, 1, 3, 1, 2, 1, 7, 4, 2, 1, 5, 1, 2, 3, 15, 1, 8, 1, 4, 3, 2, 1, 10, 6, 2, 13, 4, 1, 7, 1, 31, 3, 2, 5, 17, 1, 2, 3, 9, 1, 6, 1, 4, 10, 2, 1, 22, 8, 12, 3, 4, 1, 26, 5, 9, 3, 2, 1, 14, 1, 2, 10, 63, 5, 6, 1, 4, 3, 11, 1, 34, 1, 2, 18, 4, 7, 6, 1, 19, 40, 2, 1, 13, 5, 2, 3, 8, 1, 21, 7, 4, 3, 2, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS For n>1: a(n) = 1 iff n is prime. a(n) = A078896(n) iff n is a prime power (A000961). LINKS Michel Lagneau, Table of n, a(n) for n = 1..10000 MAPLE f:= proc(n) local p;   p:= max(numtheory:-factorset(n));   add(padic:-ordp(k, p), k=1..n); end proc: 1, seq(f(n), n=2..1000); # Robert Israel, Dec 23 2014 MATHEMATICA a[1] = 1; a[n_] := With[{p = FactorInteger[n][[-1, 1]]}, IntegerExponent[ Range[n], p] // Total]; Array[a, 100] (* Jean-François Alcover, Mar 09 2019 *) PROG (PARI) a(n) = if (n==1, 1, my(p = vecmax(factor(n)[, 1])); sum(i=1, n, valuation(i, p))); \\ Michel Marcus, Dec 23 2014, Mar 09 2019 CROSSREFS Cf. A006530, A078896, A078899. Sequence in context: A140185 A229341 A106790 * A322034 A226629 A249580 Adjacent sequences:  A078894 A078895 A078896 * A078898 A078899 A078900 KEYWORD nonn AUTHOR Reinhard Zumkeller, Dec 12 2002 STATUS approved

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Last modified June 19 11:41 EDT 2019. Contains 324219 sequences. (Running on oeis4.)