cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A326990 Sum of odd divisors of n that are greater than 1.

Original entry on oeis.org

0, 0, 3, 0, 5, 3, 7, 0, 12, 5, 11, 3, 13, 7, 23, 0, 17, 12, 19, 5, 31, 11, 23, 3, 30, 13, 39, 7, 29, 23, 31, 0, 47, 17, 47, 12, 37, 19, 55, 5, 41, 31, 43, 11, 77, 23, 47, 3, 56, 30, 71, 13, 53, 39, 71, 7, 79, 29, 59, 23, 61, 31, 103, 0, 83, 47, 67, 17, 95, 47, 71, 12, 73, 37, 123, 19, 95, 55, 79, 5
Offset: 1

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Author

Omar E. Pol, Aug 24 2019

Keywords

Comments

Also sum of nonpowers of 2 dividing n, divided the sum of powers of 2 dividing n.
a(n) = 0 iff n is a power of 2.
a(n) = n iff n is an odd prime.
First differs from A284233 at a(15).

Examples

			For n = 18 the divisors of 18 are [1, 2, 3, 6, 9, 18]. The sum of odd divisors of 18 that are greater than 1 is 3 + 9 = 12, so a(18) = 12. On the other hand, there are four divisors of 18 that are not powers of 2, they are [3, 6, 9, 18], and the sum of them is 3 + 6 + 9, 18 = 36. Also there are two divisors of 18 that are powers of 2, they are [1, 2], and the sum of them is 1 + 2 = 3. Then we have that 36/3 = 12, so a(18) = 12.
		

Crossrefs

Programs

  • Magma
    sol:=[]; m:=1; for n in [1..80] do v:=[d:d in Divisors(n)|d gt 1 and IsOdd(d)]; if #v ne 0 then sol[m]:=&+v; m:=m+1; else sol[m]:=0; m:=m+1; end if; end for; sol; // Marius A. Burtea, Aug 24 2019
  • Mathematica
    Table[Total[Select[Rest[Divisors[n]],OddQ]],{n,80}] (* Harvey P. Dale, Jan 11 2025 *)

Formula

a(n) = A000593(n) - 1.
a(n) = (A000203(n) - A038712(n))/A038712(n).
a(n) = A326988(n)/A038712(n).
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