A294386 - OEIS

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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.

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

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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;

od:

seq(A[i], i=0..N); # Robert Israel, Oct 29 2017

PROG