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%I #9 Aug 24 2015 02:36:36
%S 1,14,15,17,22,40,41,45,50,51,54,70,71,102,112,120,121,123,132,144,
%T 156,165,200,201,203,210,211,213,230,231,302,312,320,321,334,343,404,
%U 414,433,440,441,457,475,506,516,547,560,561,574,605,615
%N Numbers n such that a_1! + a_2! + ... + a_m! is a square number, where a_1a_2...a_m is the decimal expansion of n.
%F A010052(A061602(a(n)))=1. - _R. J. Mathar_, Jul 12 2007
%e 1! + 4! = 4! + 1! = 5^2, hence 14 and 41 are in the sequence.
%p A061602 := proc(n) local digs ; digs := convert(n,base,10) ; add(factorial(op(i,digs)),i=1..nops(digs)) ; end: isA130687 := proc(n) issqr(A061602(n)) ; end: for n from 1 to 3000 do if isA130687(n) then printf("%d, ",n) ; fi ; od ; # _R. J. Mathar_, Jul 12 2007
%t Select[Range[755], IntegerQ[Sqrt[DigitCount[ # ][[10]]+Sum[DigitCount[ # ][[i]]*i!, {i, 1, 9}]]] &]
%K base,nonn
%O 1,2
%A _Yalcin Aktar_, Jun 30 2007
%E Edited by _Stefan Steinerberger_ and _R. J. Mathar_, Jul 12 2007
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