This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348148 #6 Nov 01 2021 21:18:04
%S A348148 3780,66960,167400,406224,1097280,6656832,13035330,29410290,
%T A348148 4529295360,27477725184,88071903612,1159632322560,7035102756864,
%U A348148 18554223329280,22385029489560,54934276752360,112562288197632,125356165141536,307631949813216
%N A348148 Numbers k for which sigma(k)/k = 32/9.
%C A348148 This sequence will contain terms of the form 135*P and 819*Q, where P is a perfect number (A000396) not divisible by 3 or 5, and Q is a perfect number not divisible by 3, 7, or 13. Proof: sigma(135*P)/(135*P) = sigma(135)*sigma(P)/(135*P) = 240*(2*P)/(135*P) = 32/9 and sigma(819*Q)/(819*Q) = sigma(819)*sigma(Q)/(819*Q) = 1456*(2*Q)/(819*P) = 32/9. QED
%C A348148 Terms ending in "4", "32", or "80" and some terms ending in "60" will have one of these forms:
%C A348148 a( 1) = 3780 = 135* 28 = 135*A000396(2)
%C A348148 a( 2) = 66960 = 135* 496 = 135*A000396(3)
%C A348148 a( 4) = 406224 = 819* 496 = 819*A000396(3)
%C A348148 a( 5) = 1097280 = 135* 8128 = 135*A000396(4)
%C A348148 a( 6) = 6656832 = 819* 8128 = 819*A000396(4)
%C A348148 a( 9) = 4529295360 = 135* 33550336 = 135*A000396(5)
%C A348148 a(10) = 27477725184 = 819* 33550336 = 819*A000396(5)
%C A348148 a(12) = 1159632322560 = 135* 8589869056 = 135*A000396(6)
%C A348148 a(13) = 7035102756864 = 819* 8589869056 = 819*A000396(6)
%C A348148 a(14) = 18554223329280 = 135*137438691328 = 135*A000396(7)
%C A348148 a(17) = 112562288197632 = 819*137438691328 = 819*A000396(7).
%H A348148 G. P. Michon, <a href="http://www.numericana.com/answer/numbers.htm#multiperfect">Multiperfect Numbers and Hemiperfect Numbers</a>
%H A348148 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy: Some Resources (preliminary version 4)</a>
%H A348148 Walter Nissen, <a href="http://upforthecount.com/math/ffp8.html">Primitive Friendly Pairs with friends < 2^34 with denom < 20000</a>
%e A348148 167400 is a term, since sigma(167400)/167400 = 595200/167400 = 32/9.
%t A348148 Select[Range[5*10^8], DivisorSigma[1, #]/# == 32/9 &]
%t A348148 Do[If[DivisorSigma[1, k]/k == 32/9, Print[k]], {k, 5*10^8}]
%Y A348148 Cf. A000203, A000396, A211680, A212610.
%Y A348148 Subsequence of A005101 and A218416.
%K A348148 nonn
%O A348148 1,1
%A A348148 _Timothy L. Tiffin_, Oct 02 2021