

A270443


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


1



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
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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 A280687 A271774
Adjacent sequences: A270440 A270441 A270442 * A270444 A270445 A270446


KEYWORD

nonn,easy


AUTHOR

Paolo P. Lava, Mar 17 2016


STATUS

approved



