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

1,2

Comments

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

Links

Table of n, a(n) for n=1..18.

Example

     | 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  |

Maple

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);

Crossrefs

Cf. A000203, A307587.

Sequence in context: A094037 A250088 A166193 * A224743 A260542 A307218

Adjacent sequences: A307583 A307584 A307585 * A307587 A307588 A307589

Keyword

nonn,base,fini,full

Author

Paolo P. Lava, Apr 16 2019

Status

approved