A321297 a(n) is the sum of proper divisors of n that are >= sqrt(n) minus the sum of the divisors that are greater than 1 and less than sqrt(n).

0, 0, 0, 2, 0, 1, 0, 2, 3, 3, 0, 5, 0, 5, 2, 10, 0, 10, 0, 9, 4, 9, 0, 17, 5, 11, 6, 15, 0, 21, 0, 18, 8, 15, 2, 36, 0, 17, 10, 27, 0, 31, 0, 27, 16, 21, 0, 45, 7, 28, 14, 33, 0, 43, 6, 37, 16, 27, 0, 67, 0, 29, 20, 50, 8, 55, 0, 45, 20, 45, 0, 76, 0, 35, 32

Offset: 1

Author

Nathaniel J. Strout, Nov 02 2018

Keywords

• nonn

Crossrefs

Cf. A000203 (sigma), A070038, A079667.

Programs

Mathematica

Array[Function[{d, s}, 1 + Subtract @@ (Total /@ Reverse@ TakeDrop[d, LengthWhile[d, # < s &]])] @@ {Most@ Divisors[#], Sqrt@ #} &, 74, 2] (* Michael De Vlieger, Nov 25 2018 *)

PARI

a(n)=sumdiv(n, d, if(d>1&&d=n/d, d, -d)))

Formula

a(p) = 0, for primes p.

a(n) = 2*A070038(n) - sigma(n) - n + 1 for n > 1. - Andrew Howroyd, Nov 25 2018