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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

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).

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

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

CROSSREFS

Cf. A006530.

Sequence in context: A083399 A105561 A294903 * A196941 A062843 A136164

Adjacent sequences:  A087130 A087131 A087132 * A087134 A087135 A087136

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 17 2003

STATUS

approved

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Last modified May 21 09:24 EDT 2018. Contains 304377 sequences. (Running on oeis4.)