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

1,1

Comments

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

Links

Table of n, a(n) for n=1..38.

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

Adjacent sequences: A273192 A273193 A273194 * A273196 A273197 A273198

Keyword

nonn

Author

Peter Luschny, May 18 2016

Status

approved