A307587 -id:A307587 - cp's OEIS frontend

A307586 Numbers k such that the determinant of the Vandermonde matrix of their digits is equal to sigma(k), the sum of divisors of k.

1, 1349, 12673, 12934, 16748, 16874, 17034, 28957, 60438, 67180, 80612, 81257, 87021, 93651, 413856, 712530, 813624, 942786

Offset: 1

Paolo P. Lava, Apr 16 2019

Tested all the 8877691 numbers with distinct digits; no additional terms. - Giovanni Resta, Apr 16 2019

			     | 1  1   1    1     1   |
     | 1  2   4    8     16  |
det  | 1  6  36   216   1296 | = 14400  = sigma(12673).
     | 1  7  49   343   2401 |
     | 1  3   9    27    81  |

Cf. A000203, A307587.

with(numtheory): with(linalg): P:=proc(q) local a,c,k,n;
for n from 1 to q do a:=convert(n,base,10): c:=[]:
for k from 1 to nops(a) do c:=[op(c), a[-k]]; od;
if sigma(n)=det(vandermonde(c)) then print(n); fi; od; end: P(10^9);

A307651 a(n) is the determinant of the Vandermonde matrix of the digits of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, -7, -6, -5, -4, -3, -2, -1, 0

Offset: 0

Rémy Sigrist, Apr 20 2019

			             | 2^0 2^1 2^2 |
a(234) = det | 3^0 3^1 3^2 | = 2.
             | 4^0 4^1 4^2 |

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Wikipedia, Vandermonde matrix

See A307710 for the factorial base variant.

Cf. A007376, A010784, A177894, A307586, A307587.

a(n) = my (d=digits(n)); matdet(matrix(#d,#d,r,c,d[r]^(c-1)))

a(n) != 0 iff n belongs to A010784.

a(n) = 0 for any n > 9876543210.

cp's OEIS Frontend

A307586 Numbers k such that the determinant of the Vandermonde matrix of their digits is equal to sigma(k), the sum of divisors of k.

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