A227983 Numbers n such that sigma(n+1) - sigma(n-1) < sigma(n); where sigma(n) = A000203(n) = sum of the divisors of n.

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73

Offset: 1

Author

Jaroslav Krizek, Aug 08 2013

Keywords

• nonn

Comments

See A076530 - numbers n such that sigma(n+1) - sigma(n-1) = sigma(n).

Complement of union of A076530, A227982 and number 1.

Examples

			Number 60 is in the sequence because sigma(61) - sigma(59) = 62 - 60 = 2 < sigma(60) = 168.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A076530, A000203, A227982.

Programs

Mathematica

Flatten[Position[Partition[DivisorSigma[1,Range[100]],3,1],?(#[[3]]- #[[1]]< #[[2]]&),1,Heads->False]]+1 (* _Harvey P. Dale, Jul 25 2021 *)