OFFSET
1,4
COMMENTS
Noncentral 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
FORMULA
a(n) = tau(n)-2 + (tau(n) mod 2), tau = A000005.
a(n) = 2*A072670(n-1). - Omar E. Pol, Jul 08 2017
Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 3), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 14 2024
EXAMPLE
The divisors of 4 are 1, 2, 4 so the noncentral 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 noncentral divisors of 12 are 1, 2, 6, 12 because its central divisors are 3, 4.
MAPLE
MATHEMATICA
If[EvenQ[#], #-2, #-1]&/@DivisorSigma[0, Range[100]] (* Harvey P. Dale, Sep 22 2024 *)
PROG
(PARI) A161840(n) = numdiv(n)+issquare(n)-2; \\ Antti Karttunen, Jul 07 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jun 21 2009
EXTENSIONS
More terms from R. J. Mathar, Jul 04 2009
STATUS
approved