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A372574
a(n) = 1 if the squarefree part of n is congruent to 1 or 5 modulo 6, otherwise 0.
1
1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1
OFFSET
1
COMMENTS
a(n) = 1 iff A007913(n) is in A007310.
FORMULA
a(n) = A354354(A007913(n)).
Sum_{k=1..n} a(k) ~ n/2. - Amiram Eldar, May 27 2024
Multiplicative with a(p^e) = [e == 0 (mod 2)] if p <= 3 and a(p^e) = 1 if p > 3, where [ ] is the Iverson bracket.
MATHEMATICA
a[n_] := If[And @@ EvenQ[IntegerExponent[n, {2, 3}]], 1, 0]; Array[a, 100] (* Amiram Eldar, May 27 2024 *)
PROG
(PARI) A372574(n) = (1==gcd(core(n), 6));
(PARI) A372574(n) = { my(f = factor(n)); prod(k=1, #f~, if(f[k, 1]<=3, !(f[k, 2]%2), 1)); }; \\ Antti Karttunen, May 29 2024
CROSSREFS
Characteristic function of A339690.
Sequence in context: A373155 A078650 A285305 * A028863 A089012 A083035
KEYWORD
nonn,mult,easy
AUTHOR
Antti Karttunen, May 26 2024
STATUS
approved