A217769 -id:A217769 - cp's OEIS frontend

A294386 a(n) is the smallest number whose deficiency or abundance is equal to 2*n, or a(n) = 0 if such a number does not exist.

6, 3, 5, 7, 22, 11, 13, 27, 17, 19, 46, 23, 112, 58, 29, 31, 250, 57, 37, 55, 41, 43, 94, 47, 60, 106, 53, 87, 84, 59, 61, 85, 108, 67, 142, 71, 73, 712, 158, 79, 156, 83, 405, 115, 89, 141, 406, 119, 97, 202, 101, 103, 214, 107, 109, 145, 113, 177, 418, 143, 120, 243, 192, 127, 262, 131, 261, 274, 137, 139, 574, 185

Offset: 0

Michel Marcus and Omar E. Pol, Oct 29 2017

nonn

If A096502(n) <> 0, i.e., there is a prime p of the form 2^k - 2*n - 1, then 0 < a(n) <= 2^(k-1)*p since 2^(k-1)*p has deficiency 2*n. - Robert Israel, Oct 29 2017

Michel Marcus, Table of n, a(n) for n = 0..8220 (terms <= 10^10) (terms 0..1644 from Robert Israel)

Bisection of A294347.
First differs from A217769 at a(12).
Cf. A000203, A000396, A005100, A005101, A033879, A033880, A096502, A294393, A294406.

N:= 100: # to get a(0)..a(N)
count:= 0:
for n from 1 while count < N+1 do
  d:= abs(2*n - numtheory:-sigma(n));
  if d::even and d <= 2*N and not assigned(A[d/2]) then
    count:= count+1; A[d/2]:= n;
  fi
od:
seq(A[i],i=0..N); # Robert Israel, Oct 29 2017

a033879(n) = 2*n-sigma(n)
a(n) = my(k=1); while(1, if(abs(a033879(k))==2*n, return(k)); k++) \\ Felix Fröhlich, Oct 29 2017

cp's OEIS Frontend

A294386 a(n) is the smallest number whose deficiency or abundance is equal to 2*n, or a(n) = 0 if such a number does not exist.

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