%I #12 Jan 27 2017 13:20:39

%S 1,8,12,40,56,225,441

%N Refactorable numbers that are not the sum of two refactorable numbers.

%C Is this sequence finite?

%H S. Colton, <a href="https://cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2, 1999.

%H Joshua Zelinsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL5/Zelinsky/zelinsky9.html">Tau Numbers: A Partial Proof of a Conjecture and Other Results </a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8

%e 40 is a term because 40 is a refactorable number and there is no partition of 40 into two refactorable parts.

%o (PARI) isrefac(n) = (n%numdiv(n))==0;

%o isok(n) = isrefac(n) && (sum(k=1, n\2, isrefac(k) && isrefac(n-k)) == 0); \\ _Michel Marcus_, Jan 26 2017

%Y Cf. A033950, A172398, A280634.

%K nonn,more

%O 1,2

%A _Altug Alkan_, Jan 26 2017