cp's OEIS Frontend

A283757 Numbers n such that phi(n) = Sum_{j=1..k} d(n^j) for some k, where phi(n) is the Euler totient function of n and d(n) is the number of divisors of n.

%I A283757 #10 Mar 17 2017 23:11:25
%S A283757 1,3,8,10,18,24,30,435,485,579,678,759,1052,1593,3243,3857,3913,4085,
%T A283757 4445,4773,4953,5685,6078,6278,6322,6836,7570,9823,10199,10703,12474,
%U A283757 12913,12927,14180,14511,14623,16958,17013,17014,17174,17518,17966,18238,19334,19432
%N A283757 Numbers n such that phi(n) = Sum_{j=1..k} d(n^j) for some k, where phi(n) is the Euler totient function of n and d(n) is the number of divisors of n.
%C A283757 Values of k: {1, 1, 1, 1, 1, 1, 1, 4, 9, 9, 4, 5, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9, 8, 9, 9, 16, 9, 12, 12, 12, 4, 32, 12, 9, 12, 32, 12, 13, 12, 12, 12, 12, 12, 12, 9, ...}. - _Michael De Vlieger_, Mar 17 2017
%e A283757 d(1052) + d(1052^2) + d(1052^3) + d(1052^4) + d(1052^5) + d(1052^6) + d(1052^7) + d(1052^8) = 524 = phi(1052).
%p A283757 with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=0; 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 A283757 Select[Range@ 4000, Module[{k = 1, e = EulerPhi@ #, b}, While[Set[b, Sum[DivisorSigma[0, #^j], {j, k}]] < e, k++]; If[b == e, True, False]] &] (* _Michael De Vlieger_, Mar 17 2017 *)
%Y A283757 Cf. A000005, A000010, A270389, A270713, A275660.
%K A283757 nonn
%O A283757 1,2
%A A283757 _Paolo P. Lava_, Mar 16 2017