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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 k-digit number is one of the k! = A000142(k) permutations of the digits that does not begin with 0. This is to A014612 "triprimes" or "3-almost 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

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Last modified December 10 05:49 EST 2018. Contains 318044 sequences. (Running on oeis4.)