

A144563


Subset of A020342 (vampire numbers, definition 1) listing numbers which have more than one such representation of the desired form.


7



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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OFFSET

1,1


COMMENTS

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)


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..184, Nov 01 2021


FORMULA

Subsequence of A020342; contains 10*A020342 as a subsequence.  M. F. Hasler, Nov 01 2021


EXAMPLE

1260 = 21*60 = 6*210. 1395 = 5*9*31 = 15*93. 1530 = 30*51 = 3*510.


PROG

(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


CROSSREFS

Closely related: A020342, A014575, A080718, A280928, A048936.
Sequence in context: A099592 A240922 A014575 * A175746 A291714 A350375
Adjacent sequences: A144560 A144561 A144562 * A144564 A144565 A144566


KEYWORD

nonn,base,more


AUTHOR

N. J. A. Sloane, Jan 03 2009, based on email from Zak Seidov


EXTENSIONS

Corrected Anumber in definition. More terms and examples R. J. Mathar, Jan 05 2009
Terms beyond a(15) by M. F. Hasler, Nov 01 2021


STATUS

approved



