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A020342 Vampire numbers: (definition 1): n has a nontrivial factorization using n's digits. 15
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
Sean A. Irvine, Java program (github)
EXAMPLE
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
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
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Jan 03 2009
STATUS
approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)