A110597 Balanced numbers (A020492) k such that k mod 12 = 1.

1, 1045, 29029, 50065, 64285, 87685, 1390753, 2011009, 3189625, 7711405, 39298441, 53238625, 68393065, 75416341, 96345613, 225938245, 228404605, 231562825, 233591605, 279999445, 458406445, 462027565, 470527057, 491291125, 513574369, 663605761, 666373825

Offset: 1

Author

Walter Kehowski, Sep 13 2005

Keywords

• nonn

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..8224 (terms below 6.5*10^14, calculated using data from Jud McCranie)

Crossrefs

Intersection of A017533 and A020492.

Cf. A000010, A000203, A062699.

Programs

Maple

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;

Mathematica

Select[Range[10^7], Mod[#, 12] == 1 && Divisible[DivisorSigma[1, #], EulerPhi[#]] &] (* Amiram Eldar, Dec 04 2019 *)

PARI

forstep(n=1,1e5,12, if(sigma(n)%eulerphi(n)==0, print1(n", "))) \\ Charles R Greathouse IV, Nov 27 2013

Extensions

a(10)-a(27) from Donovan Johnson, Aug 30 2012