A110597 - OEIS

%I #15 Dec 04 2019 13:00:04

%S 1,1045,29029,50065,64285,87685,1390753,2011009,3189625,7711405,

%T 39298441,53238625,68393065,75416341,96345613,225938245,228404605,

%U 231562825,233591605,279999445,458406445,462027565,470527057,491291125,513574369,663605761,666373825

%N Balanced numbers (A020492) k such that k mod 12 = 1.

%C For the first 27 terms, the quotient sigma(n)/phi(n) is 1, 2 or 3.

%H Amiram Eldar, <a href="/A110597/b110597.txt">Table of n, a(n) for n = 1..8224</a> (terms below 6.5*10^14, calculated using data from Jud McCranie)

%p with(numtheory); BNM1:=[]: for z from 1 to 1 do for m from 0 to 500000 do n:=12*m+1; if sigma(n) mod phi(n) = 0 then BNM1:=[op(BNM1),n] fi; od; od; BNM1;

%t Select[Range[10^7], Mod[#, 12] == 1 && Divisible[DivisorSigma[1, #], EulerPhi[#]] &] (* _Amiram Eldar_, Dec 04 2019 *)

%o (PARI) forstep(n=1,1e5,12, if(sigma(n)%eulerphi(n)==0, print1(n", "))) \\ _Charles R Greathouse IV_, Nov 27 2013

%Y Intersection of A017533 and A020492.

%Y Cf. A000010, A000203, A062699.

%K nonn

%O 1,2

%A _Walter Kehowski_, Sep 13 2005

%E a(10)-a(27) from _Donovan Johnson_, Aug 30 2012