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 A334256 #10 Apr 21 2020 13:52:32 %S A334256 3072,1310720,469762048,48378511622144,14636698788954112, %T A334256 1115414963960152064,1254378597012249509888,358899852698093036240896, %U A334256 28472620903563746322679857152 %N A334256 Numbers k such that H(k) = 2*k, where H(k) is the number of ordered factorizations of k (A074206). %C A334256 If p is an odd prime then 2^(4*p - 2) * p is a term, hence this sequence is infinite. %C A334256 Since A074206(k) depends only on the prime signature (A124010) of k, then each term is of the form A050324(k)/2 = A074206(A025487(k))/2. %C A334256 Besides terms of the form 2^(4*p - 2) * p at least 79 terms not of this form are known. For example, 1115414963960152064 = 2^46 * 11^2 * 131 is a term not of this form. To ease the search, can we narrow the possible prime signatures of terms? %H A334256 David A. Corneth, <a href="/A334256/a334256.gp.txt">List of found terms in form of oddpart * 2^(multiplicity of 2)</a> %e A334256 3072 is a term since A074206(3072) = 6144 = 2 * 3072. %t A334256 h[1] = 1; h[n_] := h[n] = DivisorSum[n, h[#] &, # < n &]; Select[Range[1.5*10^6], h[#] == 2*# &] %o A334256 (PARI) is(n) = A074206(n) == n<<1 %Y A334256 Subsequence of A270308. %Y A334256 Cf. A074206, A122408, A163272. %Y A334256 Cf. A025487, A050324, A124010. %K A334256 nonn,more %O A334256 1,1 %A A334256 _David A. Corneth_ and _Amiram Eldar_, Apr 20 2020