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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 22:37 EDT 2019. Contains 328291 sequences. (Running on oeis4.)