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A161840 Number of non-central divisors of n. 5
0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 4, 0, 2, 2, 4, 0, 4, 0, 4, 2, 2, 0, 6, 2, 2, 2, 4, 0, 6, 0, 4, 2, 2, 2, 8, 0, 2, 2, 6, 0, 6, 0, 4, 4, 2, 0, 8, 2, 4, 2, 4, 0, 6, 2, 6, 2, 2, 0, 10, 0, 2, 4, 6, 2, 6, 0, 4, 2, 6, 0, 10, 0, 2, 4, 4, 2, 6, 0, 8, 4, 2, 0, 10, 2, 2, 2, 6, 0, 10, 2, 4, 2, 2, 2, 10, 0, 4, 4, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Non-central divisors in the following sense: if we sort the divisors of n in natural order, there is one "central", median divisor if the number of divisors tau(n) = A000005(n) is odd, and there are two "central" divisors if tau(n) is even. a(n) is the number of divisors not counting the median or two central divisors.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = tau(n)-2 + (tau(n) mod 2), tau = A000005.

a(n) = A000005(n) - A049240(n) - 1.

a(n) = A000005(n) + A010052(n) - 2.

a(n) = A000005(n) - A169695(n).

For n >= 2, a(n) = A200213(n) + 2*A010052(n). - Antti Karttunen, Jul 07 2017

a(n) = 2*A072670(n-1). - Omar E. Pol, Jul 08 2017

EXAMPLE

The divisors of 4 are 1, 2, 4 so the non-central divisors of 4 are 1, 4 because its central divisor is 2.

The divisors of 12 are 1, 2, 3, 4, 6, 12 so the non-central divisors of 12 are 1, 2, 6, 12 because its central divisors  are 3, 4.

MAPLE

A000005 := proc(n) numtheory[tau](n) ; end: A010052 := proc(n) if issqr(n) then 1; else 0 ; fi; end: A161840 := proc(n) A000005(n)+A010052(n)-2 ; end: seq(A161840(n), n=1..100) ; - R. J. Mathar, Jul 04 2009

PROG

(PARI) A161840(n) = numdiv(n)+issquare(n)-2; \\ Antti Karttunen, Jul 07 2017

(Scheme) (define (A161840 n) (+ (A000005 n) (A010052 n) -2)) ;; Antti Karttunen, Jul 07 2017

CROSSREFS

Cf. A000005, A049240, A010052, A161841, A169695, A183002, A183003, A200213.

Sequence in context: A246721 A249441 A076472 * A140302 A085341 A221474

Adjacent sequences:  A161837 A161838 A161839 * A161841 A161842 A161843

KEYWORD

easy,nonn,changed

AUTHOR

Omar E. Pol, Jun 21 2009

EXTENSIONS

More terms from R. J. Mathar, Jul 04 2009

STATUS

approved

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Last modified July 23 10:34 EDT 2017. Contains 289686 sequences.