A227760 -id:A227760 - cp's OEIS frontend

A227758 a(n) = sigma(sigma(n)) - sigma(n) - n, where sigma(n) = A000203(n) = sum of the divisors of n.

-1, -1, 0, -3, 1, 10, 0, 1, -8, 11, 5, 16, -3, 22, 21, -15, 4, -1, 3, 34, 10, 33, 13, 84, -24, 28, 23, 36, 13, 93, 0, 9, 43, 32, 41, -15, -15, 70, 25, 104, 13, 114, -3, 96, 45, 77, 29, 52, -26, -15, 72, 21, 13, 186, 68, 184, 49, 86, 49, 252, -27, 94, 43, -63

Offset: 1

Jaroslav Krizek, Jul 26 2013

sign

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]
a(n) <  0 for numbers n from A227759, a(n) >  0 for numbers n from A227760.
Sequence contains anomalous increased frequency of values 13 (see A227756).

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

Paul Tek, Table of n, a(n) for n = 1..10000

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

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

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.

Original entry on oeis.org

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

Jaroslav Krizek, Jul 29 2013

nonn

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.

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

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

A227758(a(n)) < 0.

cp's OEIS Frontend

A227758 a(n) = sigma(sigma(n)) - sigma(n) - n, where sigma(n) = A000203(n) = sum of the divisors of n.

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