

A056595


Number of nonsquare divisors of n.


17



0, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 6, 1, 3, 2, 4, 1, 7, 1, 3, 3, 3, 3, 5, 1, 3, 3, 6, 1, 7, 1, 4, 4, 3, 1, 7, 1, 4, 3, 4, 1, 6, 3, 6, 3, 3, 1, 10, 1, 3, 4, 3, 3, 7, 1, 4, 3, 7, 1, 8, 1, 3, 4, 4, 3, 7, 1, 7, 2, 3, 1, 10, 3, 3, 3, 6, 1, 10, 3, 4, 3, 3, 3, 9, 1, 4, 4, 5, 1, 7, 1
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OFFSET

1,6


COMMENTS

a(A000430(n))=1; a(A030078(n))=2; a(A030514(n))=2; a(A006881(n))=3; a(A050997(n))=3; a(A030516(n))=3; a(A054753(n))=4; a(A000290(n))=A055205(n).  Reinhard Zumkeller, Aug 15 2011


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A000005(n)  A046951(n) = tau(n)  tau(A000188(n)).


EXAMPLE

a(36)=5 because the set of divisors of 36 has tau(36)=nine elements, {1, 2, 3, 4, 6, 9, 12, 18, 36}, five of which, that is {2, 3, 6, 12, 18}, are not perfect squares.


MATHEMATICA

Table[Count[Divisors[n], _?(#!=Floor[Sqrt[#]]^2&)], {n, 110}] (* Harvey P. Dale, Jul 10 2013 *)
a[1] = 0; a[n_] := Times @@ (1 + (e = Last /@ FactorInteger[n]))  Times @@ (1 + Floor[e/2]); Array[a, 100] (* Amiram Eldar, Jul 22 2019 *)


PROG

(Haskell)
a056595 n = length [d  d < [1..n], mod n d == 0, a010052 d == 0]
 Reinhard Zumkeller, Aug 15 2011
(PARI) a(n)=sumdiv(n, d, !issquare(d)) \\ Charles R Greathouse IV, Aug 28 2016


CROSSREFS

Cf. A000005, A000188, A046951.
See A194095 and A194096 for record values and where they occur.
Sequence in context: A325116 A227339 A030777 * A160097 A252477 A029351
Adjacent sequences: A056592 A056593 A056594 * A056596 A056597 A056598


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 21 2000


STATUS

approved



