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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)