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 A066511 #18 Jul 30 2025 15:01:20
%S A066511 100,110,1806,1872,2404,3742,12488,14378,25130,26696,53418,57448,
%T A066511 61962,64938,67528,67624,172362,187624,195114,208072,591882,643624,
%U A066511 790758,938948,1361562,1381624,1803776,1877682,1892224,2091770,3335288,3559402,6585656,8810794
%N A066511 f-amicable numbers where f(n) = n-1.
%C A066511 f-amicable pairs are defined similarly to f-perfect numbers in A066218. That is, a, b is a f-amicable pair if f(a) = D(b) and f(b) = D(a), where D(n) = sum_{k divides n, k<n} f(d).
%C A066511 Equivalently, let g(n) = sigma(n)-n-d(n)+2, where d(n) is the number of divisors of n and sigma(n) is their sum. Then n is in the sequence if g(g(n))=n but g(n) != n. (Sequence A066230 contains the solutions of g(n)=n.)
%H A066511 Amiram Eldar, <a href="/A066511/b066511.txt">Table of n, a(n) for n = 1..162</a>
%H A066511 J. Pe, <a href="https://vixra.org/abs/2503.0165">On a Generalization of Perfect Numbers</a>, J. Rec. Math., 31(3) (2002-2003), 168-172.
%e A066511 Proper divisors of 100 = {1, 2, 4, 5, 10, 20, 25, 50}. f applied to these divisors = {0, 1, 3, 4, 9, 19, 24, 49}; their sum = 109. So D(100) = f(110). proper divisors of 110 = {1, 2, 5, 10, 11, 22, 55}. f applied to these divisors = {0, 1, 4, 9, 10, 21, 54}; their sum = 99. So D(110) = f(100). Therefore 100, 110 is an f-amicable pair.
%t A066511 g[ n_ ] := DivisorSigma[ 1, n ]-n-DivisorSigma[ 0, n ]+2; For[ n=1, True, n++, If[ g[ g[ n ] ]==n&&g[ n ]!=n, Print[ n ] ] ]
%Y A066511 Cf. A066230, A066218.
%K A066511 nonn
%O A066511 1,1
%A A066511 _Joseph L. Pe_, Jan 04 2002
%E A066511 Edited by _Dean Hickerson_, Jan 10 2002.
%E A066511 More terms from _Amiram Eldar_, Oct 02 2019