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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
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?
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.
Sequence in context: A183726 A137485 A251786 * A262459 A205623 A205358
KEYWORD
nonn,more
AUTHOR
STATUS
approved