A227759 Numbers n such that A227758(n) = sigma(sigma(n)) - sigma(n) - n < 0, where sigma(n) = A000203(n) = sum of the divisors of n

1, 2, 4, 9, 13, 16, 18, 25, 36, 37, 43, 49, 50, 61, 64, 67, 73, 81, 97, 98, 100, 109, 121, 144, 151, 157, 163, 169, 181, 193, 211, 225, 229, 241, 242, 256, 277, 283, 289, 313, 324, 331, 337, 338, 361, 373, 397, 400, 409, 421, 433, 441, 457, 484, 487, 523, 529

Offset

1,2

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 A227760, where A000668 = Mersenne primes, A227760 = numbers n such that sigma(sigma(n)) - sigma(n) - n > 0.

Links

Table of n, a(n) for n=1..57.

Formula

A227758(a(n)) < 0.

Example

Number 16 is in sequence because sigma(sigma(16)) - sigma(16) - 16 = 32 - 31 - 16 = -15 < 0.

Crossrefs

Cf. A000203, A051027, A000668, A227760, A227758.

Sequence in context: A098009 A129376 A266582 * A343216 A320514 A210640

Adjacent sequences: A227756 A227757 A227758 * A227760 A227761 A227762

Keyword

nonn

Author

Jaroslav Krizek, Jul 29 2013

Status

approved