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A283759 Numbers whose Euler totient function is equal to the product of the number of divisors of their k first powers, for some k.

%I A283759 #9 Mar 21 2017 04:44:28
%S A283759 3,7,8,10,18,24,30,57,74,344,399,494,518,629,654,679,1154,2408,2989,
%T A283759 3048,3175,3458,3789,4218,4578,4890,5022,7668,10602,13720,14647,14701,
%U A283759 14837,15613,16133,17563,17945,18335,19608,20195,20358,21243,21336,21423,22083,22503
%N A283759 Numbers whose Euler totient function is equal to the product of the number of divisors of their k first powers, for some k.
%C A283759 Values of k: {1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 3, 3, 3, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, ...}. - _Michael De Vlieger_, Mar 17 2017
%H A283759 Paolo P. Lava, <a href="/A283759/b283759.txt">Table of n, a(n) for n = 1..150</a>
%e A283759 phi(629) = 576 and d(629) * d(629^2) * d(629^3) = 4 * 9 * 16= 576;
%e A283759 phi(14647) = 14400 and d(14647) * d(14647^2) * d(14647^3) * d(14647^4) = 4 * 9 * 16 * 25 = 14400.
%p A283759 with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=1; k:=0; while a<phi(n) do k:=k+1; a:=a*tau(n^k); if phi(n)=a then print(n); break; fi; od; od; end: P(10^5);
%t A283759 Select[Range[2, 25000], Module[{k = 1, e = EulerPhi@ #, b}, While[Set[b, Product[DivisorSigma[0, #^j], {j, k}]] < e, k++]; If[b == e, True, False]] &] (* _Michael De Vlieger_, Mar 17 2017 *)
%Y A283759 Cf. A000005, A000010, A270389, A270713, A275660, A283757, A283758.
%K A283759 nonn
%O A283759 1,1
%A A283759 _Paolo P. Lava_, Mar 16 2017