A175854 Number of anagrams of n that are divisible by exactly 3 primes (counted with multiplicity).

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

Offset

1

Comments

An anagram of a k-digit number is a permutation of the digits that does not begin with 0.

This is to A014612, as A131371 is to semiprimes A001358, and as A046810 is to primes A000040.

The first term > 1 is a(103)=2.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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.

Maple

N:= 10^3:
TP:= select(t -> numtheory:-bigomega(t)=3, {$1..N}):
f:= proc(n) local L, d, w, x, i;
      L:= convert(n, base, 10); d:= nops(L);
      L:= select(t -> t[-1] <> 0, combinat:-permute(L));
      L:= map(t-> add(t[i]*10^(i-1), i=1..d), L);
      nops(convert(L, set) intersect TP)
end proc:
map(f, [$1..N]); # Robert Israel, Jan 15 2024

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: A169673 A101605 A358753 * A353678 A135133 A011712

Adjacent sequences: A175851 A175852 A175853 * A175855 A175856 A175857

Keyword

nonn,easy,base

Author

Jonathan Vos Post, Jan 24 2011

Status

approved