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

1,4

Links

Table of n, a(n) for n=1..75.

Formula

a(p) = 0, for primes p.

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

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 *)

Prog

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

Crossrefs

Cf. A000203 (sigma), A070038, A079667.

Sequence in context: A340503 A072662 A030010 * A343156 A163577 A132178

Adjacent sequences: A321294 A321295 A321296 * A321298 A321299 A321300

Keyword

nonn

Author

Nathaniel J. Strout, Nov 02 2018

Status

approved