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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 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.