A057564 - OEIS

A057564

Natural numbers n for which the following three properties hold: (i) Phi[Sigma[n]]=2*phi(n), (ii) Sigma[n-2]=2*Sigma[Phi[n-2]], (iii) Sigma[n+2]=2*Sigma[Phi[n+2]].

666, 19674, 309114, 369594, 715194, 1180026, 1924794, 2722266, 2741274, 4261914, 5564826, 6296634, 6623226, 6826266, 7206906, 9726648, 15956154, 16046874, 16478874, 19263546, 25333146, 27706554, 28151514, 32938074

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OFFSET

1,1

COMMENTS

Called "Beastly neighbors" because 666 is the least element of the sequence and because these numbers are seen to have a symmetric relationship with their two "neighbors," using analogy to numbering houses on the same side of the street (e.g. 664 and 668 are "neighbors" of 666).

REFERENCES

D. Iannucci, "The neighbors of the Beast," Journal of Recreational Mathematics, Volume 31, Number 1, 2002, pp. 52-55.

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

Phi[Sigma[666]]=Phi[1482]=432=2*216=2*Phi[666], Sigma[664]=1260=2*630=2*Sigma[328]=Sigma[Phi[664]], Sigma[668]=1176=2*588=2*Sigma[332]=Sigma[Phi[668]]. Thus 666 is an element of the sequence.

MATHEMATICA

Select[Range[33*10^6], EulerPhi[DivisorSigma[1, #]]==2EulerPhi[#]&&DivisorSigma[ 1, #-2]==2DivisorSigma[1, EulerPhi[#-2]]&&DivisorSigma[ 1, #+2] == 2DivisorSigma[1, EulerPhi[#+2]]&] (* Harvey P. Dale, Aug 04 2020 *)

CROSSREFS

Sequence in context: A183655 A104181 A221014 * A227490 A171114 A328551

Adjacent sequences: A057561 A057562 A057563 * A057565 A057566 A057567

KEYWORD

easy,nonn

AUTHOR

Douglas E. Iannucci, Oct 04 2000

STATUS

approved