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 A237428 #32 Jun 29 2025 01:06:29
%S A237428 6,126,3808,19360,104320,4317184,126764640,1920554064,3710312448
%N A237428 Numbers k with following property: List all proper divisors of k. Replace any composite number in the list with its proper divisors. Repeat. Sum of remaining numbers (1's and primes) is equal to k.
%C A237428 Is there a largest term? Is there any odd term?
%C A237428 a(8) if it exists is greater than 10^9. - _Giovanni Resta_, Feb 07 2014
%C A237428 Composite numbers k such that k = A074206(k) + Sum_{p|k} (p-1)*A074206(k/p). - _Charlie Neder_, Jun 02 2019
%e A237428 6 is a term because: 1 + 2 + 3 = 6.
%e A237428 126 is a term because: [1 + 2 + 3 + (6 - 6) + 7 + (9 - 9) + (14 - 14) + (18 - 18) + (21 - 21) + (42 - 42) + (63 - 63)] + [1 + 2 + 3] + [1 + 3] + [1 + 2 + 7] + [1 + 2 + 3 + (6 - 6) + (9 - 9)] + [1 + 3 + 7] + [1 + 2 + 3 + (6 - 6) + 7 + (14 - 14) + (21 - 21)] + [1 + 3 + 7 + (9 - 9) + (21 - 21)] + [1 + 2 + 3] + [1 + 3] + [1 + 2 + 3] + [1 + 2 + 7] + [1 + 3 + 7] + [1 + 3] + [1 + 3 + 7] = 126.
%t A237428 v[n_] := If[PrimeQ@n, 1, Block[{s = Sum[If[e == 1 || PrimeQ@e, e, v@e], {e, Most@ Divisors@n}]}, If[n < 1000, v[n] = s, s]]]; Select[Range@ 20000, # == v@# &] (* _Giovanni Resta_, Feb 07 2014 *)
%Y A237428 Cf. A000203, A000396, A001065, A002033, A032741, A074206, A191150.
%K A237428 nonn,more
%O A237428 1,1
%A A237428 _Lechoslaw Ratajczak_, Feb 07 2014
%E A237428 a(6)-a(7) from _Giovanni Resta_, Feb 07 2014
%E A237428 a(8)-a(9) from _Amiram Eldar_, Jun 28 2025