cp's OEIS Frontend

A270389 Numbers that are equal to the sum of the number of divisors of their k first powers, for some k.

%I A270389 #27 Jun 09 2017 09:19:56
%S A270389 1,2,5,64,203,505,524,649,818,1295,2469,2869,4355,5048,6083,10415,
%T A270389 14909,15021,22329,27433,29189,29369,35719,38023,44099,48229,56372,
%U A270389 85329,85343,89270
%N A270389 Numbers that are equal to the sum of the number of divisors of their k first powers, for some k.
%H A270389 Charles R Greathouse IV, <a href="/A270389/b270389.txt">Table of n, a(n) for n = 1..200</a>
%H A270389 Paolo P. Lava, <a href="/A270389/a270389.txt">First 30 terms with k value</a>
%F A270389 Solutions of the equation n = Sum_{i=1..k}{d(n^k)}.
%e A270389 d(1^1) = 1;
%e A270389 d(2^1) = 2;
%e A270389 d(5^1) + d(5^2) = 2 + 3 = 5;
%e A270389 d(64^1) + d(64^2) + d(64^3) + d(64^4) = 7 + 13 + 19 + 25 = 64;
%e A270389 d(203^1) + d(203^2) + d(203^3)+ d(203^4)+ d(203^5)+ d(203^6)+ d(203^7) = 4 + 9 + 16 + 25 + 36 + 49 + 64 = 203.
%p A270389 with(numtheory): P:=proc(q) local a,k,n;
%p A270389 for n from 1 to q do a:=0; k:=0;
%p A270389 while a<n do k:=k+1; a:=a+tau(n^k); od; if n=a then print(n); fi;
%p A270389 od; end: P(10^6);
%t A270389 Select[Range[10^4], Function[n, IntegerQ@ SelectFirst[Range@ 25, Total@ Map[DivisorSigma[0, #] &, n^Range[#]] == n &]]] (* _Michael De Vlieger_, Mar 17 2016, Version 10 *)
%o A270389 (PARI) is(n)=my(e=factor(n)[,2],k,t); while(t<n, k++; t += prod(i=1,#e, k*e[i]+1)); t==n \\ _Charles R Greathouse IV_, Mar 31 2016
%Y A270389 Cf. A000005, A270713.
%K A270389 nonn
%O A270389 1,2
%A A270389 _Paolo P. Lava_, Mar 16 2016