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 A087133 Number of divisors of n that are not greater than the greatest prime-factor of n; a(1)=1. 2
 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 3, 2, 2, 3, 2, 4, 3, 3, 2, 3, 2, 3, 2, 4, 2, 4, 2, 2, 3, 3, 3, 3, 2, 3, 3, 4, 2, 5, 2, 4, 3, 3, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 3, 2, 5, 2, 3, 3, 2, 3, 5, 2, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 5, 2, 4, 2, 3, 2, 6, 3, 3, 3, 5, 2, 4, 3, 4, 3, 3, 3, 3, 2, 3, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n > 1, a(n) is the index of the greatest prime factor of n among the divisors of n (see A027750). - Michel Marcus, Jan 21 2019 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 Eric Weisstein's World of Mathematics, Divisor Function Eric Weisstein's World of Mathematics, Greatest Prime Factor FORMULA a(n) <= A000005(n), a(n)=A000005(n) iff n is prime or n=1; a(n)=2 iff n > 1 is a prime power (A000961); a(A087134(n))=n and a(k) < n for k < A087134(n). EXAMPLE n=28: gpf(28)=7 and divisors = {1,2,4,7,14,28}: 1<=7, 2<=7, 4<=7 and 7<=7, therefore a(28)=4. MATHEMATICA Table[Count[Divisors[n], _?(#<=FactorInteger[n][[-1, 1]]&)], {n, 100}] (* Harvey P. Dale, May 01 2016 *) PROG (PARI) a(n) = if (n==1, 1, my(f = factor(n), gpf = f[#f~, 1]); sumdiv(n, d, d <= gpf)); \\ Michel Marcus, Sep 21 2014 (PARI) a(n) = if (n==1, 1, vecsearch(divisors(n), vecmax(factor(n)[, 1]))); \\ Michel Marcus, Jan 21 2019 CROSSREFS Cf. A000005, A006530, A027750, A000961, A087134. Sequence in context: A083399 A105561 A294903 * A324292 A196941 A062843 Adjacent sequences:  A087130 A087131 A087132 * A087134 A087135 A087136 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 17 2003 STATUS approved

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Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)