cp's OEIS Frontend

A087133 Number of divisors of n that are not greater than the greatest prime-factor of n; a(1)=1.

%I A087133 #21 Feb 16 2025 08:32:51
%S A087133 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,
%T A087133 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,
%U A087133 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
%N A087133 Number of divisors of n that are not greater than the greatest prime-factor of n; a(1)=1.
%C A087133 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
%H A087133 Antti Karttunen, <a href="/A087133/b087133.txt">Table of n, a(n) for n = 1..65537</a>
%H A087133 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>
%H A087133 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>
%F A087133 a(n) <= A000005(n), a(n)=A000005(n) iff n is prime or n=1;
%F A087133 a(n)=2 iff n > 1 is a prime power (A000961);
%F A087133 a(A087134(n))=n and a(k) < n for k < A087134(n).
%e A087133 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.
%t A087133 Table[Count[Divisors[n],_?(#<=FactorInteger[n][[-1,1]]&)],{n,100}] (* _Harvey P. Dale_, May 01 2016 *)
%o A087133 (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
%o A087133 (PARI) a(n) = if (n==1, 1, vecsearch(divisors(n), vecmax(factor(n)[,1]))); \\ _Michel Marcus_, Jan 21 2019
%Y A087133 Cf. A000005, A006530, A027750, A000961, A087134.
%K A087133 nonn
%O A087133 1,2
%A A087133 _Reinhard Zumkeller_, Aug 17 2003