OFFSET
1,2
COMMENTS
Companion sequences are numbers the absolute value of whose deficiency is a perfect number, numbers the absolute value of whose deficiency is an abundant number. Every nonnegative integer is in one of these three sequences.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
a(1) = 1 because the deficiency of 1 is 1, and 1 is itself a deficient number.
a(10) = 12 because the deficiency of 12 is -4 and | -4 | = 4 is a deficient number.
7 is not in the sequence because the deficiency of 7 is 6, and 6 is a perfect number.
13 is not in the sequence because the deficiency of 13 is 12, and 12 is an abundant number.
MATHEMATICA
Deficiency[n_] := 2 n - DivisorSigma[1, n]; Select[Range[150], Deficiency[Abs[Deficiency[#]]] > 0 &]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Jan 21 2011
STATUS
approved