

A175854


Number of anagrams of n that are divisible by exactly 3 primes (counted with multiplicity).


1



0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1


COMMENTS

An anagram of a kdigit number is one of the k! = A000142(k) permutations of the digits that does not begin with 0. This is to A014612 "triprimes" or "3almost primes", as A131371 is to semiprimes A001358, and as A046810 is to primes A000040.
The first term > 1 is a(103)=2.


LINKS

Table of n, a(n) for n = 1..100


EXAMPLE

a(125) = 1 because 125 = 5^3 is divisible by exactly 3 primes (counted with multiplicity); 152 = 2^3 * 19 is in A014613 (quadruprimes); 215 = 5 * 43 is a semiprime; 251 is prime; 512 = 2^9; and 521 is prime.


PROG

(Sage)
concat = lambda x: Integer(''.join(map(str, x)))
def A175854(n):
....d3 = lambda x: sum(m for p, m in factor(x)) == 3
....return sum(1 for p in Permutations(n.digits()) if p[0] != 0 and d3(concat(p))) # [D. S. McNeil, Jan 25 2011]


CROSSREFS

Cf. A000040, A000142, A001358, A014612, A046810, A131371.
Sequence in context: A187946 A188436 A293162 * A185708 A286996 A275305
Adjacent sequences: A175851 A175852 A175853 * A175855 A175856 A175857


KEYWORD

nonn,easy,base


AUTHOR

Jonathan Vos Post, Jan 24 2011


STATUS

approved



