A175888 Numbers n with property that sigma(n) < min(sigma(n-2),sigma(n-1),sigma(n+1),sigma(n+2)).

11, 17, 23, 29, 37, 41, 47, 53, 59, 67, 71, 79, 83, 89, 97, 101, 107, 113, 121, 127, 131, 137, 143, 149, 157, 163, 167, 173, 179, 187, 191, 197, 203, 211, 217, 223, 227, 233, 239, 247, 251, 257, 263, 269, 277, 281, 289, 293, 299, 307, 311, 317, 323, 331, 337

Offset

1,1

Comments

Strict local minimums of sigma(n) of the 2nd order:

sigma(n) is less than any of 4 closest neighbors.

b(n) = the first term ending with n=1..9:

11,22683662,23,17254,635,69686,17,6143138,29

c(n) = position of b(n) in the sequence:

1,3781722,3,2872,105,11608,2,1024132,4.

The term in the sequence ending with zero should be very large (>~10^80 according to Charles R Greathouse IV).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

sminQ[{a_, b_, c_, d_, e_}]:=c<Min[{a, b, d, e}]; Flatten[ Position[ Partition[ DivisorSigma[ 1, Range[400]], 5, 1], _?sminQ]]+2 (* Harvey P. Dale, Aug 12 2014 *)

Prog

(PARI) {for(n=3, 10^10, sigma(n)<vecmin([sigma(n-2), sigma(n-1),
sigma(n+1), sigma(n+2)])&print(n, ", "))}

Crossrefs

Cf. A000203 sigma(n) = sum of divisors of n.

Sequence in context: A106574 A171125 A156781 * A209624 A243153 A280326

Adjacent sequences: A175885 A175886 A175887 * A175889 A175890 A175891

Keyword

nonn

Author

Zak Seidov, Oct 08 2010

Status

approved