cp's OEIS Frontend

A270443 Least m such that d(n^m) > n, where d(n) is the number of divisors of n.

%I A270443 #9 Mar 30 2016 02:48:47
%S A270443 2,3,2,5,2,7,3,5,3,11,2,13,3,3,4,17,3,19,3,4,4,23,3,13,5,9,4,29,3,31,
%T A270443 7,5,5,5,3,37,6,6,4,41,3,43,4,5,6,47,3,25,5,7,5,53,4,7,4,7,7,59,3,61,
%U A270443 7,5,11,8,4,67,6,8,4,71,4,73,8,6,6,8,4,79,4,21
%N A270443 Least m such that d(n^m) > n, where d(n) is the number of divisors of n.
%C A270443 a(p) = p for any prime p.
%H A270443 Paolo P. Lava, <a href="/A270443/b270443.txt">Table of n, a(n) for n = 2..500</a>
%e A270443 d(4^1) = 3, d(4^2) = 5 then a(4) = 2;
%e A270443 d(9^1) = 3, d(9^2) = 5, d(9^3) = 7, d(9^4) = 9, d(9^5) = 11, then a(9) = 5.
%p A270443 with(numtheory): P:=proc(q) local a,k,n;
%p A270443 for n from 2 to q do a:=tau(n); k:=1;
%p A270443 while a<n do k:=k+1; a:=tau(n^k); od; print(a); od; end: P(10^6);
%t A270443 nn = 100; Table[SelectFirst[Range@ nn, DivisorSigma[0, n^#] > n &], {n, 2, nn}] (* _Michael De Vlieger_, Mar 17 2016, Version 10 *)
%o A270443 (PARI) a(n) = {p=1; until (numdiv(n^p) > n, p++); p;} \\ _Michel Marcus_, Mar 17 2016
%Y A270443 Cf. A000005, A270337, A270389.
%K A270443 nonn,easy
%O A270443 2,1
%A A270443 _Paolo P. Lava_, Mar 17 2016