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A144563
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Subset of A020342 (vampire numbers, definition 1) listing numbers which have more than one such representation of the desired form.
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7
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1260, 1395, 1530, 6880, 12060, 12550, 12600, 13950, 14350, 15030, 15300, 18270, 21870, 31590, 37840, 68800, 102510, 102550, 104260, 105210, 105250, 105264, 105750, 112590, 114390, 116928, 118440, 118480, 119682, 120060, 120600, 123840, 125050, 125460, 125500, 125950
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listen;
history;
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OFFSET
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1,1
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COMMENTS
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From M. F. Hasler, Nov 01 2021: (Start)
If x is in A020342, then 10*x is in this sequence, and this makes up most of the terms. Exceptions are the terms not ending in 0, {1395, 105264, 116928, 119682, 192375, 258795, 263736, 268398, 289674, 1008126, 1133484, 1173939, ...}. There are terms of the form 10*x in A020342 with x not in A020342, like {25510, 45760, 67950, 136590, 146520, 168520, 175560, 246150, 250510, 255010, ...}. Is any such term in this sequence A144563, or can it be proved there isn't?
All terms have at least 3 distinct prime factors (omega, A001221), and 4 prime factors counted with multiplicity (bigomega, A001222). The squarefree terms are {132430, 174370, 1012990, 1073290, 1094730, 1156990, 1170670, 117393, ...}. (End)
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LINKS
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M. F. Hasler, Table of n, a(n) for n = 1..184, Nov 01 2021
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FORMULA
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Subsequence of A020342; contains 10*A020342 as a subsequence. - M. F. Hasler, Nov 01 2021
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EXAMPLE
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1260 = 21*60 = 6*210. 1395 = 5*9*31 = 15*93. 1530 = 30*51 = 3*510.
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PROG
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(PARI) /* Helper function: count number of representations of n as product of numbers >= m whose multiset of digits is D, excluding the trivial representation if m = 0. */
VampRepCount(n, m=0, D=vecsort(digits(n)))={ if(#D<3, m && (D[1]>=m && vecprod(D)==n || vecsort(digits(n))==D), n >= m^2, my(S=Set(D), c=m && vecsort(digits(n))==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 && c += VampRepCount(n\f, f, C) ); c, n >= m && vecsort(digits(n))==D)}
is_A144563(n)=VampRepCount(n)>1 \\ M. F. Hasler, Nov 01 2021
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CROSSREFS
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Closely related: A020342, A014575, A080718, A280928, A048936.
Sequence in context: A099592 A240922 A014575 * A175746 A291714 A350375
Adjacent sequences: A144560 A144561 A144562 * A144564 A144565 A144566
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KEYWORD
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nonn,base,more
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AUTHOR
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N. J. A. Sloane, Jan 03 2009, based on email from Zak Seidov
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EXTENSIONS
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Corrected A-number in definition. More terms and examples R. J. Mathar, Jan 05 2009
Terms beyond a(15) by M. F. Hasler, Nov 01 2021
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STATUS
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approved
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