A126078 Numbers such that the sum of the factorials of the digits of the fifth power is a square.

1, 396, 849, 1000, 2807, 4274, 4565, 4971, 5000, 6030, 6487, 6942, 7281, 8210, 11163, 11847, 11895, 15015, 17682, 19043, 19584, 19586, 20500, 20577, 20957, 21315, 23000, 23188, 23397, 25747, 27121, 27720, 29241, 29399, 32160, 34233, 35234

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..534

Example

a(2) = 396, 396^5 = 9738138110976, 9! + 7! + 3! + 8! + 1! + 3! + 8! + 1! + 1! + 0! + 9! + 7! + 6! = 817216 = 904^2.

Maple

a:=proc(n) local nn: nn:=convert(n^5, base, 10): if type(sqrt(add(nn[j]!, j=1..nops(nn))), integer)=true then n else fi end: seq(a(n), n=1..45000); # Emeric Deutsch, Mar 06 2007

Mathematica

Select[Range[50000], IntegerQ[Sqrt[Total[IntegerDigits[#^5]!]]]&] (* Vincenzo Librandi, Mar 29 2014 *)

Crossrefs

Sequence in context: A278606 A230450 A247989 * A275171 A028299 A205628

Adjacent sequences: A126075 A126076 A126077 * A126079 A126080 A126081

Keyword

nonn,base

Author

Yalcin Aktar, Mar 02 2007

Extensions

More terms from Emeric Deutsch, Mar 06 2007

Name changed by Franklin T. Adams-Watters, Mar 29 2014

Status

approved