

A334256


Numbers k such that H(k) = 2*k, where H(k) is the number of ordered factorizations of k (A074206).


1




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

Table of n, a(n) for n=1..9.
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



