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A273195 The determinant of the difference table of the divisors vanishes for these numbers. 0
10, 28, 50, 99, 110, 130, 170, 171, 190, 196, 222, 230, 250, 290, 310, 370, 410, 430, 470, 476, 530, 532, 550, 590, 610, 644, 650, 670, 710, 730, 790, 812, 830, 850, 868, 890, 950, 970 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Prime power-like numbers (A273200) have nonvanishing determinants.
LINKS
EXAMPLE
50 is in this sequence because the determinant of DTD(50) = 0.
[ 1 2 5 10 25 50]
[ 1 3 5 15 25 0]
[ 2 2 10 10 0 0]
[ 0 8 0 0 0 0]
[ 8 -8 0 0 0 0]
[-16 0 0 0 0 0]
MATHEMATICA
selQ[n_] := Module[{d = Divisors[n], ld}, ld = Length[d]; Det @ Table[ PadRight[ Differences[d, k], ld], {k, 0, ld-1}] == 0];
Select[Range[1000], selQ] (* Jean-François Alcover, Jul 15 2019 *)
PROG
(Sage)
def is_A273195(n):
D = divisors(n)
T = matrix(ZZ, len(D))
for (m, d) in enumerate(D):
T[0, m] = d
for k in range(m-1, -1, -1) :
T[m-k, k] = T[m-k-1, k+1] - T[m-k-1, k]
return T.det() == 0
print([n for n in range(1, 1000) if is_A273195(n)])
CROSSREFS
Cf. A273200.
Sequence in context: A082286 A088407 A267012 * A069953 A113746 A177720
KEYWORD
nonn
AUTHOR
Peter Luschny, May 18 2016
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)