A207376 Sum of central divisors of n.

1, 3, 4, 2, 6, 5, 8, 6, 3, 7, 12, 7, 14, 9, 8, 4, 18, 9, 20, 9, 10, 13, 24, 10, 5, 15, 12, 11, 30, 11, 32, 12, 14, 19, 12, 6, 38, 21, 16, 13, 42, 13, 44, 15, 14, 25, 48, 14, 7, 15, 20, 17, 54, 15, 16, 15, 22, 31, 60, 16, 62, 33, 16, 8, 18, 17, 68, 21, 26, 17

Offset

1,2

Comments

If n is a square (A000290) then a(n) = sqrt(n) because the squares have only one central divisor. If n is a prime p then a(n) = 1 + p = A000203(n). For the number of central divisors of n see A169695.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

Omar E. Pol, Illustration of the divisors of the first 12 positive integers

Formula

a(n) = A000203(n) - A323643(n). - Omar E. Pol, Feb 26 2019

Example

For n = 12 the divisors of 12 are 1, 2, 3, 4, 6, 12. The central (or middle) divisors of 12 are 3 and 4, so a(12) = 3 + 4 = 7.

Mathematica

cdn[n_]:=Module[{dn=Divisors[n], len}, len=Length[dn]; Which[ IntegerQ[ Sqrt[n]], Sqrt[n], PrimeQ[n], n+1, OddQ[len], dn[[Floor[len/2]+1]], EvenQ[len], dn[[len/2]]+dn[[len/2+1]]]]; Array[cdn, 70] (* Harvey P. Dale, Nov 07 2012 *)

Crossrefs

Row sums of A207375. Where records occur give A008578.

Cf. A000005, A000040, A000203, A000290, A027750, A161840, A169695, A323643.

Sequence in context: A139524 A247413 A108127 * A213197 A378127 A049277

Adjacent sequences: A207373 A207374 A207375 * A207377 A207378 A207379

Keyword

nonn,easy

Author

Omar E. Pol, Feb 23 2012

Status

approved