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A336040
Characteristic function of refactorable numbers (A033950).
10
1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0
OFFSET
1,1
LINKS
FORMULA
a(n) = 1 - ceiling(n/d(n)) + floor(n/d(n)), where d(n) is the number of divisors of n (A000005).
a(n) = [A054008(n) == 0], where [ ] is the Iverson bracket. - Antti Karttunen, Nov 24 2021
a(p) = 0 for odd primes p. - Wesley Ivan Hurt, Nov 28 2021
EXAMPLE
a(1) = 1 since d(1) = 1 and 1 divides 1.
a(2) = 1 since d(2) = 2 and 2 divides 2.
a(3) = 0 since d(3) = 2, but 2 does not divide 3.
MATHEMATICA
a[n_] := Boole @ Divisible[n, DivisorSigma[0, n]]; Array[a, 100] (* Amiram Eldar, Jul 08 2020 *)
PROG
(PARI) a(n) = n%numdiv(n) == 0; \\ Michel Marcus, Jul 07 2020
CROSSREFS
Cf. A000005, A033950, A054008, A336041 (inverse Möbius transform), A335182, A335665, A349322.
Sequence in context: A011654 A016348 A015556 * A359769 A359770 A015780
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jul 07 2020
STATUS
approved