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 A307587 Numbers k such that the determinant of the Vandermonde matrix of their digits is equal to phi(k), the Euler totient function of k. 2

%I #13 Apr 19 2019 18:37:52

%S 1,2,190,280,480,1073,1674,1736,4850,15867,16230,16302,23715,24056,

%T 25064,35712,52976,54730,75184,105342,456382,964325

%N Numbers k such that the determinant of the Vandermonde matrix of their digits is equal to phi(k), the Euler totient function of k.

%C Tested all the 8877691 numbers with distinct digits; no additional terms. - _Giovanni Resta_, Apr 16 2019

%e | 1 1 1 |

%e det | 1 9 81 | = 72 = phi(190).

%e | 1 0 0 |

%p with(numtheory): with(linalg): P:=proc(q) local a,c,k,n;

%p for n from 1 to q do a:=convert(n,base,10): c:=[]:

%p for k from 1 to nops(a) do c:=[op(c), a[-k]]; od;

%p if phi(n)=det(vandermonde(c)) then print(n); fi; od; end: P(10^9);

%Y Cf. A000005, A307586.

%K nonn,base,fini,full

%O 1,2

%A _Paolo P. Lava_, Apr 16 2019

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Last modified September 15 03:44 EDT 2024. Contains 375931 sequences. (Running on oeis4.)