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%I #11 Apr 03 2014 11:35:08
%S 1,6,747,2802,10000,10256,11876,13875,14623,14710,17117,18090,23919,
%T 26569,34282,35402,40515,41202,41850,42195,44684,48396,54698,58509,
%U 59293,59644,59900,65502,67795,74004,75320,79593,82677,82713,83402
%N Numbers n with following property: suppose n^6 = d1 d2 d3 ...dk in decimal; then d1! + d2! + ... + dk! is a square.
%C Numbers n such that n^6 is in A130687.
%e a(2) = 6, because 6^6 = 46656, and (4!+6!+6!+5!+6!)^(1/2) = 48 is an integer.
%p A061602 := proc(n) local digs ; digs := convert(n,base,10) ; add(factorial(op(i,digs)),i=1..nops(digs)) ; end: isA130687 := proc(n) RETURN(issqr(A061602(n))) ; end: isA130688 := proc(n) RETURN(isA130687(n^6)) ; end: for n from 1 to 130000 do if isA130688(n) then printf("%d, ",n) ; fi : od:
%o (PARI) for(n=1,10^5,m=n^6;s=0;while(m,s+=(m%10)!;m\=10);if(issquare(s),print1(n",")))
%Y Cf. A130687, A089185, A126076, A126077, A126078.
%K nonn,base
%O 1,2
%A _Yalcin Aktar_, Jun 30 2007
%E Edited by _R. J. Mathar_ and _Martin Fuller_, Jul 13 2007
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