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

0,1

Comments

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

Links

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

Maple

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

Prog

(PARI) 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

Crossrefs

Bisection of A294347.

First differs from A217769 at a(12).

Cf. A000203, A000396, A005100, A005101, A033879, A033880, A096502, A294393, A294406.

Sequence in context: A199728 A199867 A171030 * A217769 A296501 A296491

Adjacent sequences: A294383 A294384 A294385 * A294387 A294388 A294389

Keyword

nonn

Author

Michel Marcus and Omar E. Pol, Oct 29 2017

Status

approved