

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
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OFFSET

1


COMMENTS

After a(1) = 1 numbers such that only primes occur as exponents in their prime factorization.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for characteristic functions
Index entries for sequences computed from exponents in factorization of n


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)))))


CROSSREFS

Cf. A010051, A056166, A095683, A095691, A101436, A125070, A126849.
Sequence in context: A205633 A252488 A170956 * A307424 A075802 A307423
Adjacent sequences: A293446 A293447 A293448 * A293450 A293451 A293452


KEYWORD

nonn,mult


AUTHOR

Antti Karttunen, Nov 17 2017


STATUS

approved



