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 A112343 #22 Apr 07 2024 17:40:02
%S A112343 1,30,70,84,120,126,180,198,264,286,308,468,520,624,646,880,884,912,
%T A112343 1008,1150,1224,1350,1566,1672,1748,1798,2484,2576,2784,2900,3135,
%U A112343 3348,3400,3526,3570,3600,4104,4320,4606,4752,5600,5704,5920,6032,6068,6279
%N A112343 Positive integers m such that the largest prime-power divisor of m equals the sum of the other maximal prime-power divisors (> 1) of m.
%C A112343 Sequence consists of those positive integers m where, if m = Product_{p prime, p|m} p^k(p), each k(p) = positive integer, then Sum_{p prime, p|m} p^k(p) = twice the largest prime power dividing m. The inclusion of 1 in the sequence is debatable.
%C A112343 There is substantial overlap between the terms here and in A298010, which has a straightforward cause in the two definitions. Initially (looking at the 46 terms currently in the data section) the majority of the terms that are in A298010 but not here are the oblong (a.k.a. pronic) numbers, A002378; and the terms that are here but not in A298010 are in the subsequence A071312, except for the "debatable" 1. The 2nd term not in A071312 or A298010 is 7980. - _Peter Munn_, Apr 07 2024
%H A112343 Michael De Vlieger, <a href="/A112343/b112343.txt">Table of n, a(n) for n = 1..10000</a>
%e A112343 84 = 2^2 * 3 * 7. Now 7 = 2^2 + 3, so 84 is in the sequence.
%e A112343 120 = 2^3 * 3 * 5. Now 2^3 = 3 + 5, so 120 is in the sequence.
%t A112343 f[n_] := Block[{pp}, If[n == 1, Return[True]]; pp = Power @@@ FactorInteger[n]; Return[2Max[pp] == Plus @@ pp]; ]; Select[Range[6500], f] (* _Ray Chandler_, Dec 04 2005 *)
%Y A112343 Cf. A008475, A034699, A298010.
%Y A112343 A071312 is a subsequence.
%K A112343 nonn
%O A112343 1,2
%A A112343 _Leroy Quet_, Dec 01 2005
%E A112343 Edited by _Ray Chandler_, Dec 04 2005