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A287059 Least numbers k > 1 such that k'' = n*k', where k' and k'' are the first and the second arithmetic derivatives of k. 0

%I #11 May 28 2017 09:35:11

%S 2,4,12,160,1255,256,12279,3072,1113823,119120,2191040,4640768,

%T 1835008,12805120,134217728

%N Least numbers k > 1 such that k'' = n*k', where k' and k'' are the first and the second arithmetic derivatives of k.

%e a(3) = 160 because 160'' / 160' = 1296 / 432 = 3 and this is the least number to have this property.

%p with(numtheory): P:=proc(q) local a,b,k,n,p; for n from 0 to q do

%p for k from 2 to q do a:=k*add(op(2,p)/op(1,p),p=ifactors(k)[2]); b:=a*add(op(2,p)/op(1,p),p=ifactors(a)[2]); if b=n*a then print(k); break;

%p fi; od; od; end: P(10^9);

%Y Cf. A003415, A068346.

%K nonn,more

%O 0,1

%A _Paolo P. Lava_, May 19 2017

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Last modified July 19 17:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)