OFFSET
1,24
COMMENTS
a(n) = 0 if n is a prime power.
From Michael De Vlieger, Sep 15 2015: (Start)
Let k be a divisor d | n such that d^2 < n and d^2 does not divide n.
a(n) <= A010846(n), as any k is regular to n, i.e., k is a product less than n of the prime divisors of n.
a(n) <= A045763(n), as any k neither divides nor is coprime to n.
a(n) <= A243822(n), as any k is a "semidivisor" of n, i.e., k is a product less than n of the prime divisors of n that do not divide n.
(End)
a(n) = 0 if and only if n is a prime power (A000961). - Robert Israel, Sep 22 2015
From Robert Israel, Oct 22 2015: (Start)
a(n) = 1 if n = p^i * q^j where p and q are distinct primes and 1 <= i,j <= 2, i.e. n is in A006881, A054753 or A085986.
This appears to be "if and only if". (End)
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
a(6) = 1 because (1, 4, 9, 36) are squares of divisors of 6 and only 4 is proper non-divisor of 6.
MAPLE
f:= n -> nops(select(t -> (t^2 < n) and (n mod t^2 <> 0), numtheory:-divisors(n))):
map(f, [$1..100]); # Robert Israel, Sep 22 2015
MATHEMATICA
f[n_] := Block[{d = Divisors@ n}, Select[d^2, And[Mod[n, #] != 0, # < n] &]]; Length@ f@ # & /@ Range@ 120 (* Michael De Vlieger, Sep 15 2015 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d^2 < n) && (n % d^2)); \\ Michel Marcus, Sep 15 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Sep 15 2015
EXTENSIONS
Definition and a(80) corrected by Charles R Greathouse IV, Sep 15 2015
STATUS
approved