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.

%I A307586 #14 Apr 19 2019 18:37:44
%S A307586 1,1349,12673,12934,16748,16874,17034,28957,60438,67180,80612,81257,
%T A307586 87021,93651,413856,712530,813624,942786
%N 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.
%C A307586 Tested all the 8877691 numbers with distinct digits; no additional terms. - _Giovanni Resta_, Apr 16 2019
%e A307586      | 1  1   1    1     1   |
%e A307586      | 1  2   4    8     16  |
%e A307586 det  | 1  6  36   216   1296 | = 14400  = sigma(12673).
%e A307586      | 1  7  49   343   2401 |
%e A307586      | 1  3   9    27    81  |
%p A307586 with(numtheory): with(linalg): P:=proc(q) local a,c,k,n;
%p A307586 for n from 1 to q do a:=convert(n,base,10): c:=[]:
%p A307586 for k from 1 to nops(a) do c:=[op(c), a[-k]]; od;
%p A307586 if sigma(n)=det(vandermonde(c)) then print(n); fi; od; end: P(10^9);
%Y A307586 Cf. A000203, A307587.
%K A307586 nonn,base,fini,full
%O A307586 1,2
%A A307586 _Paolo P. Lava_, Apr 16 2019