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A174961 Number of non-unitary divisors of a nonsquarefree number n. 1
1, 2, 1, 2, 3, 2, 2, 4, 1, 2, 2, 4, 5, 4, 2, 2, 6, 1, 2, 2, 4, 4, 4, 2, 5, 2, 8, 2, 2, 6, 3, 4, 4, 4, 2, 8, 2, 2, 5, 4, 8, 6, 2, 2, 8, 1, 2, 2, 4, 6, 4, 4, 4, 4, 11, 2, 2, 4, 4, 2, 4, 8, 6, 2, 8, 1, 2, 2, 2, 6, 10, 4, 2, 4, 10, 5, 4, 8, 4, 2, 6, 2, 12, 4, 8, 5, 4, 4, 4, 2, 12, 2, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Essentially the nonzero terms of A048105.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = d(n) - 2^omega(n) where d(n) is the divisor function(A000005) and omega(n) is the number of distinct prime factors of n(A001221).

EXAMPLE

For n = 4, the fourth non-unitary number is 12 (see A013929). 12 = 2^2*3 and the nonsquarefree terms 4 and 12 are obtained from (2-1)(1+1) = 2.

MATHEMATICA

Select[Table[DivisorSigma[0, n] - 2^(PrimeNu[n]), {n, 1, 500}], # > 0 &] (* G. C. Greubel, May 21 2017 *)

CROSSREFS

Sequence in context: A082860 A283845 A058071 * A104889 A290979 A117910

Adjacent sequences:  A174958 A174959 A174960 * A174962 A174963 A174964

KEYWORD

nonn

AUTHOR

N. Wu (neil_wu0626(AT)yahoo.com), Apr 02 2010

STATUS

approved

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)