A261556 Numbers that divide the sum of the product of the factorials of their digits and the sum of the factorials of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 17, 54, 86, 573, 768, 999, 6143, 94584, 159287, 27167549, 40548073, 72382636, 131092614, 340720926, 1161216721, 2955383683, 3892089702, 5304046976, 6554754648, 72338498624, 279445396448, 331043595868, 466026097373, 962499474063, 3082891291712

Offset

1,2

Links

Table of n, a(n) for n=1..35.

Example

54 is in the list because 5! = 120, 4! = 24,  120*24=2880, 120+24=144, 2880+144=3024, 3024/54=56.

Mathematica

fQ[n_] := Block[{d = IntegerDigits[n]!}, Mod[Times @@ d + Total@ d, n] == 0]; Select[Range@ 1000000, fQ] (* Michael De Vlieger, Aug 26 2015 *)

Prog

(PARI) isok(n) = my(d = digits(n)); ((sum(k=1, #d, d[k]!)+prod(k=1, #d, d[k]!)) % n) == 0; \\ Michel Marcus, Aug 25 2015

Crossrefs

Cf. A197181, A247227.

Sequence in context: A283161 A165165 A075776 * A033088 A307498 A034294

Adjacent sequences: A261553 A261554 A261555 * A261557 A261558 A261559

Keyword

nonn,base

Author

Paolo Omodei-Zorini, Aug 24 2015

Extensions

a(24)-a(25) from Jon E. Schoenfield, Aug 24 2015

a(26)-a(30) from Giovanni Resta, Aug 26 2015

a(31)-a(34) from Chai Wah Wu, May 04 2019

a(35) from Giovanni Resta, Aug 19 2019

Status

approved