A273195 The determinant of the difference table of the divisors vanishes for these numbers.

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

Offset: 1

Author

Peter Luschny, May 18 2016

Keywords

• nonn

Comments

Prime power-like numbers (A273200) have nonvanishing determinants.

Examples

			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]
		

Crossrefs

Cf. A273200.

Programs

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 *)

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)])