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

1,2

Links

Table of n, a(n) for n=1..51.

Formula

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

Example

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

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}]]] &]

Crossrefs

Sequence in context: A206447 A293792 A308974 * A173687 A114962 A278979

Adjacent sequences: A130684 A130685 A130686 * A130688 A130689 A130690

Keyword

base,nonn

Author

Yalcin Aktar, Jun 30 2007

Extensions

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

Status

approved