|
|
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
|
|
|
FORMULA
|
a(n)=2 iff n > 1 is a prime power (A000961);
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|