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

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, 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, 7, 5, 11, 8, 4, 67, 6, 8, 4, 71, 4, 73, 8, 6, 6, 8, 4, 79, 4, 21

Offset: 2

Author

Paolo P. Lava, Mar 17 2016

Keywords

• nonn
• easy

Comments

a(p) = p for any prime p.

Examples

			d(4^1) = 3, d(4^2) = 5 then a(4) = 2;
d(9^1) = 3, d(9^2) = 5, d(9^3) = 7, d(9^4) = 9, d(9^5) = 11, then a(9) = 5.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 2..500

Crossrefs

Cf. A000005, A270337, A270389.

Programs

Maple

with(numtheory): P:=proc(q) local a,k,n;
for n from 2 to q do a:=tau(n); k:=1;
while a
				

Mathematica

nn = 100; Table[SelectFirst[Range@ nn, DivisorSigma[0, n^#] > n &], {n, 2, nn}] (* Michael De Vlieger, Mar 17 2016, Version 10 *)

PARI

a(n) = {p=1; until (numdiv(n^p) > n, p++); p;} \\ Michel Marcus, Mar 17 2016