A126077 Numbers such that the sum of the factorials of the digits of the fourth power is a square.
1, 39, 100, 200, 305, 590, 652, 700, 1207, 1270, 1900, 2302, 2491, 4666, 6697, 9282, 10188, 10480, 11853, 12421, 13630, 13866, 14043, 14208, 14963, 15739, 15740, 18300, 18543, 18951, 20064, 21185, 21737, 23233, 24396, 24945, 25131, 25657
Offset: 1
Examples
a(2)=39, 39^4 = 2313441, (2! + 3! + 1! + 3! + 4! + 4! + 1!) = 64 = 8^2.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..700
Programs
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Maple
a:=proc(n) local nn: nn:=convert(n^4,base,10): if type(sqrt(add(nn[j]!,j=1..nops(nn))),integer)=true then n else fi end: seq(a(n),n=1..32000); # Emeric Deutsch, Mar 06 2007
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Mathematica
Select[Range[26000],IntegerQ[Sqrt[Total[IntegerDigits[#^4]!]]]&] (* Harvey P. Dale, Feb 22 2011 *)
Extensions
More terms from Emeric Deutsch, Mar 06 2007
Name changed by Franklin T. Adams-Watters, Mar 29 2014