A227758 - OEIS

%I #14 Jul 30 2013 14:18:01

%S -1,-1,0,-3,1,10,0,1,-8,11,5,16,-3,22,21,-15,4,-1,3,34,10,33,13,84,

%T -24,28,23,36,13,93,0,9,43,32,41,-15,-15,70,25,104,13,114,-3,96,45,77,

%U 29,52,-26,-15,72,21,13,186,68,184,49,86,49,252,-27,94,43,-63

%N a(n) = sigma(sigma(n)) - sigma(n) - n, where sigma(n) = A000203(n) = sum of the divisors of n.

%C Conjecture: a(n) = 0 for Mersenne primes (A000668). [This is easily proved: For Mersenne primes n=2^p-1, sigma(n)=n+1=2^p, sigma(2^p)=2^(p+1)-1, thus a(n)=0. - M. F. Hasler, Jul 30 2013]

%C a(n) <  0 for numbers n from A227759, a(n) >  0 for numbers n from A227760.

%C Sequence contains anomalous increased frequency of values 13 (see A227756).

%H Paul Tek, <a href="/A227758/b227758.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A051027(n) - A000203(n) - n.

%e For n = 6; a(n) = sigma(sigma(6)) - sigma(6) - 6 = 28 - 12 - 6 = 10.

%Y Cf. A051027, A000203, A000668, A227759, A227760, A227756.

%K sign

%O 1,4

%A _Jaroslav Krizek_, Jul 26 2013