A130687 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.

1, 14, 15, 17, 22, 40, 41, 45, 50, 51, 54, 70, 71, 102, 112, 120, 121, 123, 132, 144, 156, 165, 200, 201, 203, 210, 211, 213, 230, 231, 302, 312, 320, 321, 334, 343, 404, 414, 433, 440, 441, 457, 475, 506, 516, 547, 560, 561, 574, 605, 615

Offset: 1

Author

Yalcin Aktar, Jun 30 2007

Keywords

• base
• nonn

Examples

			1! + 4! = 4! + 1! = 5^2, hence 14 and 41 are in the sequence.
		

Programs

Maple

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

Mathematica

Select[Range[755], IntegerQ[Sqrt[DigitCount[ # ][[10]]+Sum[DigitCount[ # ][[i]]*i!, {i, 1, 9}]]] &]

Formula

A010052(A061602(a(n)))=1. - R. J. Mathar, Jul 12 2007

Extensions

Edited by Stefan Steinerberger and R. J. Mathar, Jul 12 2007