A076774 2-nadirs of sigma: numbers k such that sigma(k-2) > sigma(k-1) > sigma(k) < sigma(k+1) < sigma(k+2).

17254, 27754, 68914, 69686, 82774, 92366, 111266, 133706, 152426, 194426, 267994, 277586, 359974, 387694, 389726, 429274, 448174, 452726, 457766, 471626, 474146, 522026, 527066, 531334, 554126, 567386, 595594, 610226, 674246, 674974

Offset

1,1

Comments

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[3, 10^6], DivisorSigma[1, # - 2] > DivisorSigma[1, # - 1] > DivisorSigma[1, # ] < DivisorSigma[1, # + 1] < DivisorSigma[1, # + 2] &]
Flatten[Position[Partition[DivisorSigma[1, Range[675000]], 5, 1], _? (#[[1]]> #[[2]]>#[[3]]<#[[4]]<#[[5]]&), 1, Heads->False]]+2 (* Harvey P. Dale, Jan 04 2022 *)

Prog

(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

Crossrefs

Cf. A000203.

Sequence in context: A043621 A334310 A293478 * A236447 A094413 A209967

Adjacent sequences: A076771 A076772 A076773 * A076775 A076776 A076777

Keyword

nonn

Author

Joseph L. Pe, Nov 14 2002

Status

approved