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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
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).
Sequence in context: A373548 A199867 A171030 * A217769 A296501 A296491
KEYWORD
nonn
AUTHOR
Michel Marcus and Omar E. Pol, Oct 29 2017
STATUS
approved