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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 15:01 EST 2021. Contains 349526 sequences. (Running on oeis4.)