A227760 Numbers n such that A227758(n) = sigma(sigma(n)) - sigma(n) - n > 0, where sigma(n) = A000203(n) = sum of the divisors of n.

5, 6, 8, 10, 11, 12, 14, 15, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87

Offset: 1

Author

Jaroslav Krizek, Jul 29 2013

Keywords

• nonn

Comments

Numbers n such that A051027(n) - A000203(n) - n < 0, where A000203(n) = sum of the divisors of n , A051027(n) = A000203(A000203(n)) = sigma(sigma(n)) = sum of the divisors of the sum of the divisors of n.

Conjecture: a(n) = complement of union A000668 and A227759, where A000668 = Mersenne primes, A227759 = numbers n such that sigma(sigma(n)) - sigma(n) - n < 0.

Examples

			Number 15 is in sequence because sigma(sigma(15)) - sigma(15) - 15 = 60 - 24 - 15 = 21 > 0.
		

Crossrefs

Cf. A000203, A051027, A000668, A227759, A227758.

Programs

Mathematica

sgmaQ[n_]:=Module[{s=DivisorSigma[1,n]},Positive[DivisorSigma[1,s]-s-n]]; Select[Range[100],sgmaQ] (* Harvey P. Dale, Aug 08 2013 *)

Formula

A227758(a(n)) > 0.