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A020342 Vampire numbers: (definition 1): n has a nontrivial factorization using n's digits. 13
126, 153, 688, 1206, 1255, 1260, 1395, 1435, 1503, 1530, 1827, 2187, 3159, 3784, 6880, 10251, 10255, 10426, 10521, 10525, 10575, 11259, 11439, 11844, 11848, 12006, 12060, 12384, 12505, 12546, 12550, 12595, 12600, 12762, 12768, 12798, 12843, 12955, 12964 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Nontrivial means that there must be at least two factors.

REFERENCES

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.

LINKS

Ely Golden, Table of n, a(n) for n = 1..1000

Ely Golden, General program for generating vampire number sequences

Gordon Hamilton, Three integer sequences from recreational mathematics, Video (2013).

EXAMPLE

E.g., 1395 = 31*9*5.

MATHEMATICA

fQ[n_] := Block[{i = Sort@ IntegerDigits@ n, d = Most@ Divisors@ n, w = Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ n], s}, s = Union@ Subsets@ w; MemberQ[Map[Sort@ Flatten@ IntegerDigits@ # &, #], i] &@ DeleteCases[#, m_ /; First@ m == 1] &@ Union@ Map[Flatten[#, 1] &, Join[Map[Function[k, Map[Sort[{k}~Join~#] &, Select[s, k (Times @@ #) == n &]]], d], Map[{#, n/#} &, TakeWhile[d, # <= Sqrt@ n &]]]]]; Select[Range@ 13000, fQ] (* Michael De Vlieger, Jan 27 2017 *)

CROSSREFS

Closely related: A014575, A080718, A280928, A048936, A144563.

Sequence in context: A025388 A025389 A025380 * A179482 A009944 A203566

Adjacent sequences:  A020339 A020340 A020341 * A020343 A020344 A020345

KEYWORD

nonn,base

AUTHOR

David W. Wilson

EXTENSIONS

Edited by N. J. A. Sloane, Jan 03 2009

STATUS

approved

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Last modified May 23 22:04 EDT 2017. Contains 286937 sequences.