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A055212 Number of composite divisors of n. 7
0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 3, 0, 3, 0, 3, 1, 1, 0, 5, 1, 1, 2, 3, 0, 4, 0, 4, 1, 1, 1, 6, 0, 1, 1, 5, 0, 4, 0, 3, 3, 1, 0, 7, 1, 3, 1, 3, 0, 5, 1, 5, 1, 1, 0, 8, 0, 1, 3, 5, 1, 4, 0, 3, 1, 4, 0, 9, 0, 1, 3, 3, 1, 4, 0, 7, 3, 1, 0, 8, 1, 1, 1, 5, 0, 8, 1, 3, 1, 1, 1, 9, 0, 3, 3, 6, 0, 4, 0, 5, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

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

FORMULA

a(n) = tau(n)-omega(n)-1, where tau=A000005 and omega=A001221. - Reinhard Zumkeller, Jun 13 2003

G.f.: -x/(1 - x) + Sum_{k>=1} (x^k - x^prime(k))/((1 - x^k)*(1 - x^prime(k))). - Ilya Gutkovskiy, Mar 21 2017

EXAMPLE

a[20] = 3 because the composite divisors of 20 are 4, 10, 20.

MATHEMATICA

Table[ Count[ PrimeQ[ Divisors[n] ], False] - 1, {n, 1, 105} ]

Table[Count[Divisors[n], _?CompositeQ], {n, 120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 09 2018 *)

PROG

(Haskell)

a055212 = subtract 1 . a033273  -- Reinhard Zumkeller, Sep 15 2015

(PARI) a(n) = numdiv(n) - omega(n) - 1; \\ Michel Marcus, Oct 17 2015

CROSSREFS

Complement of A083399.

A033273(n-1) - 1.

Cf. A137944, A137945.

Sequence in context: A114206 A073202 A294904 * A028422 A064577 A322435

Adjacent sequences:  A055209 A055210 A055211 * A055213 A055214 A055215

KEYWORD

easy,nonn

AUTHOR

Leroy Quet, Jun 23 2000

STATUS

approved

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)