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

1,1

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.

Links

Table of n, a(n) for n=1..66.

Formula

A227758(a(n)) > 0.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A271728 A247047 A218866 * A055592 A242731 A151976

Adjacent sequences: A227757 A227758 A227759 * A227761 A227762 A227763

Keyword

nonn

Author

Jaroslav Krizek, Jul 29 2013

Status

approved