

A207376


Sum of central divisors of n.


4



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
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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 A049277 A214917
Adjacent sequences: A207373 A207374 A207375 * A207377 A207378 A207379


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Feb 23 2012


STATUS

approved



