A076774 - OEIS

%I #11 Sep 08 2022 08:45:07

%S 17254,27754,68914,69686,82774,92366,111266,133706,152426,194426,

%T 267994,277586,359974,387694,389726,429274,448174,452726,457766,

%U 471626,474146,522026,527066,531334,554126,567386,595594,610226,674246,674974

%N 2-nadirs of sigma: numbers k such that sigma(k-2) > sigma(k-1) > sigma(k) < sigma(k+1) < sigma(k+2).

%C I call n a "k-nadir" (or nadir of depth k) of the arithmetical function f if n satisfies f(n-k) > ... > f(n-1) > f(n) < f(n+1) < ... < f(n+k).

%H Amiram Eldar, <a href="/A076774/b076774.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[3, 10^6], DivisorSigma[1, # - 2] > DivisorSigma[1, # - 1] > DivisorSigma[1, # ] < DivisorSigma[1, # + 1] < DivisorSigma[1, # + 2] &]

%t Flatten[Position[Partition[DivisorSigma[1,Range[675000]],5,1],_? (#[[1]]> #[[2]]>#[[3]]<#[[4]]<#[[5]]&),1,Heads->False]]+2 (* _Harvey P. Dale_, Jan 04 2022 *)

%o (Magma) ds:=DivisorSigma; f:=func<n|ds(1,n) lt ds(1,n+1) and ds(1,n+1) lt ds(1,n+2)>; f1:= func<n|ds(1,n) lt ds(1,n-1) and ds(1,n-1) lt ds(1,n-2)>; [k:k in [3..675000]|f(k) and f1(k)]; // _Marius A. Burtea_, Feb 19 2020

%Y Cf. A000203.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Nov 14 2002