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A020342
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Vampire numbers: (definition 1): n has a nontrivial factorization using n's digits.
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15
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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
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1,1
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COMMENTS
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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
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REFERENCES
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Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.
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LINKS
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EXAMPLE
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1395 = 31*9*5, so 1395 is a term.
179739 = 7 * 9 * 9 * 317 so 179739 is a term. - Sean A. Irvine, Feb 28 2023
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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