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

2,1

Comments

a(p) = p for any prime p.

Links

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

Example

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.

Maple

with(numtheory): P:=proc(q) local a, k, n;
for n from 2 to q do a:=tau(n); k:=1;
while a<n do k:=k+1; a:=tau(n^k); od; print(a); od; end: P(10^6);

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A270337, A270389.

Sequence in context: A094757 A095171 A343004 * A096776 A347043 A280687

Adjacent sequences: A270440 A270441 A270442 * A270444 A270445 A270446

Keyword

nonn,easy

Author

Paolo P. Lava, Mar 17 2016

Status

approved