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%I #33 Dec 23 2024 14:53:42
%S 16,27,150
%N The number n equals the product of two numbers: sums of prime factors of n, with and without repetition.
%C Numbers n such that n = A008472(n)*A001414(n) (= sum of distinct prime factors of n, times sum of prime factors of n with repetition). - _M. F. Hasler_, May 05 2013
%H Max Alekseyev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-May/011115.html">Proof of finiteness of A073396</a>, SeqFan Mailing List, May 4, 2013.
%F a(n) = A073395(a(n)).
%F A073396 = { n | n = A008472(n)*A001414(n) }. - _M. F. Hasler_, May 05 2013
%e A073395(150) = A073395(2*3*5*5) = A008472(2*3*5*5)*A001414(2*3*5*5) = (2+3+5)*(2+3+5+5) = 10*15 = 150, therefore 150 is a term.
%t okQ[n_] := n>1 && With[{f = FactorInteger[n]}, n == Total[Times @@@ f]* Total[f[[All, 1]]]];
%t Select[Range[1000], okQ] (* _Jean-François Alcover_, Apr 06 2021 *)
%Y Cf. A008472, A001414.
%K nonn,full,fini,bref
%O 1,1
%A _Reinhard Zumkeller_, Jul 30 2002
%E Proof that there are no further terms added by _Max Alekseyev_, May 04 2013