

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.


2



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
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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]sn]]; 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



