The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A334256 Numbers k such that H(k) = 2*k, where H(k) is the number of ordered factorizations of k (A074206). 1
 3072, 1310720, 469762048, 48378511622144, 14636698788954112, 1115414963960152064, 1254378597012249509888, 358899852698093036240896, 28472620903563746322679857152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is an odd prime then 2^(4*p - 2) * p is a term, hence this sequence is infinite. 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. 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? LINKS David A. Corneth, List of found terms in form of oddpart * 2^(multiplicity of 2) EXAMPLE 3072 is a term since A074206(3072) = 6144 = 2 * 3072. MATHEMATICA h[1] = 1; h[n_] := h[n] = DivisorSum[n, h[#] &, # < n &]; Select[Range[1.5*10^6], h[#] == 2*# &] PROG (PARI) is(n) = A074206(n) == n<<1 CROSSREFS Subsequence of A270308. Cf. A074206, A122408, A163272. Cf. A025487, A050324, A124010. Sequence in context: A183726 A137485 A251786 * A262459 A205623 A205358 Adjacent sequences: A334253 A334254 A334255 * A334257 A334258 A334259 KEYWORD nonn,more AUTHOR David A. Corneth and Amiram Eldar, Apr 20 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 25 22:04 EDT 2023. Contains 361529 sequences. (Running on oeis4.)