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 A127654 #15 Mar 11 2023 05:42:14
%S A127654 66,78,244,292,476,482,578,648,680,688,770,784,832,864,956,958,976,
%T A127654 1168,1354,1360,1392,1488,1600,1658,1670,1906,2232,2264,2294,2376,
%U A127654 2480,2552,2572,2576,2626,2712,2732,2806,2842,2870,2904,2912,2992,3024,3096,3140,3172
%N A127654 Unitary aspiring numbers.
%C A127654 A unitary aspiring number is an integer whose unitary aliquot sequences ends by meeting a unitary-perfect number (A098185) in its trajectory, but is not unitary-perfect itself. There are 1693 such numbers <=100000 and of these 82860 and 97020 generate the longest unitary aliquot sequences (according to A097032), each having length 18 and ending with the unitary perfect number 90.
%H A127654 Amiram Eldar, <a href="/A127654/b127654.txt">Table of n, a(n) for n = 1..10000</a>
%H A127654 Herman J. J. te Riele, <a href="https://ir.cwi.nl/pub/9137">Unitary Aliquot Sequences</a>, MR 139/72, Mathematisch Centrum, Amsterdam, 1972.
%H A127654 Herman J. J. te Riele, <a href="https://ir.cwi.nl/pub/9068">Further Results on Unitary Aliquot Sequences</a>, NW 2/73, Mathematisch Centrum, Amsterdam, 1973.
%e A127654 a(5) = 476 because the fifth non-unitary-perfect number whose unitary aliquot sequence ends in a unitary-perfect number is 476.
%t A127654 UnitaryDivisors[n_Integer?Positive] := Select[Divisors[n], GCD[ #, n/# ] == 1 \ &]; sstar[n_] := Plus @@ UnitaryDivisors[ n] - n; g[n_] := If[n > 0, sstar[n], 0]; UnitaryTrajectory[n_] := Most[NestWhileList[ g, n, UnsameQ, All]]; UnitaryPerfectNumberQ[0] = 0; UnitaryPerfectNumberQ[k_] := If[sstar[k] == k, True, False]; UnitaryAspiringNumberQ[k_] := If[UnitaryPerfectNumberQ[Last[ UnitaryTrajectory[k]]] && ! UnitaryPerfectNumberQ[k], True, False]; Select[Range[2500], UnitaryAspiringNumberQ[ # ] &]
%t A127654 s[n_] := Times @@ (1 + Power @@@ FactorInteger[n]) - n; s[0] = s[1] = 0; q[n_] := Module[{v = NestWhileList[s, n, UnsameQ, All]}, v[[-1]] != n && v[[-2]] == v[[-1]] > 0]; Select[Range[3200], q] (* _Amiram Eldar_, Mar 11 2023 *)
%Y A127654 Cf. A002827, A097032, A127652, A097010, A098185, A127653, A063991, A097037, A097036.
%K A127654 nonn
%O A127654 1,1
%A A127654 _Ant King_, Jan 24 2007
%E A127654 More terms from _Amiram Eldar_, Mar 11 2023