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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Nontrivial means that there must be at least two factors. For any a(n), 10*a(n) is also in the sequence, and also in A144563. - M. F. Hasler, Nov 01 2021 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 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 *) PROG (PARI) is_A020342(n, m=0, D=vecsort(digits(n)))={ if(m && n >= m && vecsort(digits(n))==D, 1, #D<3, m && (D[1]>=m && vecprod(D)==n), n >= m^2, my(S=Set(D), i, C); fordiv(n, f, f < m && next; f*f > n && break; setminus(Set(digits(f)), S) && next; C=D; foreach(digits(f), d, if(i=vecsearch(C, d), C=C[^i], next(2))); C && is_A020342(n\f, f, C) && return(1)))} \\ See A144563 for a function counting the multiplicity of the representation. - M. F. Hasler, Nov 01 2021 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 EXTENSIONS Edited by N. J. A. Sloane, Jan 03 2009 STATUS approved

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)