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A273195
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The determinant of the difference table of the divisors vanishes for these numbers.
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0
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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
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OFFSET
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1,1
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COMMENTS
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Prime power-like numbers (A273200) have nonvanishing determinants.
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LINKS
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EXAMPLE
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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]
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MATHEMATICA
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selQ[n_] := Module[{d = Divisors[n], ld}, ld = Length[d]; Det @ Table[ PadRight[ Differences[d, k], ld], {k, 0, ld-1}] == 0];
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PROG
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(Sage)
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)])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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