

A020342


Vampire numbers: (definition 1): n has a nontrivial factorization using n's digits.


14



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
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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



