A065986 - OEIS

%I #18 Sep 08 2022 08:45:04

%S 6,147,286,376,534,738,805,2392,2406,4324,8214,9606,10362,12126,16263,

%T 17511,27639,29151,39215,48616,60687,61132,61915,141526,142610,147890,

%U 153530,160748,189501,212134,221121,253022,324650,326691,368296,404716,453699

%N Numbers n such that Sigma(n) = EulerPhi(n+1) + EulerPhi(n) + EulerPhi(n-1).

%H Jon E. Schoenfield, <a href="/A065986/b065986.txt">Table of n, a(n) for n = 1..80</a> (first 60 terms from Harry J. Smith)

%e Sigma(6) = 12 = 6 + 2 + 4 = EulerPhi(7) + EulerPhi(6) + EulerPhi(5).

%t Select[Range@500000, EulerPhi@(# + 1) + EulerPhi@(#) + EulerPhi@(# - 1) == DivisorSigma[1, #] &] (* _Vincenzo Librandi_, Jun 17 2018 *)

%o (PARI) { n=e1=e2=0; for (m=2, 10^9, e2=e1; e1=e; e=eulerphi(m+1); if (sigma(m) == e + e1 + e2, write("b065986.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Nov 05 2009

%o (Magma) [n: n in [2..10^6] | EulerPhi(n+1)+EulerPhi(n)+ EulerPhi(n-1) eq SumOfDivisors(n)]; // _Vincenzo Librandi_, Jun 17 2018

%Y Cf. A000010.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Dec 10 2001