login
A293449
Characteristic function for A056166, numbers that have no nonprime exponents present in their prime factorization n = p_1^e_1 * ... * p_k^e_k.
3
1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
1
COMMENTS
After a(1) = 1 numbers such that only primes occur as exponents in their prime factorization.
FORMULA
Multiplicative with a(p^e) = A010051(e).
a(1) = 1, for n > 1, a(n) = A010051(A067029(n)) * a(A028234(n)).
a(n) = 1 iff A125070(n) = 0.
EXAMPLE
For n = 4 = 2^2, 2 is prime, thus a(4) = 1.
For n = 12 = 2^2 * 3^1, 2 is prime, but 1 is not, thus a(12) = 0.
For n = 16 = 2^4, 4 is not prime, thus a(16) = 0.
For n = 72 = 2^3 * 3^2, both exponents 3 and 2 are primes, thus a(72) = 1.
MATHEMATICA
{1}~Join~Array[Boole[AllTrue[FactorInteger[#][[All, -1]], PrimeQ]] &, 104, 2] (* Michael De Vlieger, Nov 17 2017 *)
PROG
(PARI)
vecproduct(v) = { my(m=1); for(i=1, #v, m *= v[i]); m; };
A293449(n) = vecproduct(apply(e -> isprime(e), factorint(n)[, 2]));
(Scheme) (define (A293449 n) (if (= 1 n) n (* (A010051 (A067029 n)) (A293449 (A028234 n)))))
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 17 2017
STATUS
approved