A275819 Least number k such that the number of its divisors is n times the number of its prime factors, counted with multiplicity.

2, 60, 210, 2160, 1260, 77760, 4620, 12600, 18480, 3456000, 27720, 4730880, 302400, 453600, 120120, 1990656000, 180180, 1238630400, 997920, 1108800, 10644480, 1146617856000, 720720, 2494800, 70963200, 3880800, 2882880, 11415217766400, 5821200, 18602577100800

Offset

2,1

Comments

Offset is 2 because there is no solution to A000005(k) = 1 * A001222(k).

Apart from the first term all the others are multiples of 3.

Links

Giovanni Resta, Table of n, a(n) for n = 2..45

Formula

Least solution k of the equation A000005(k) = n * A001222(k).

Example

a(6) = 1260 because the number of divisors of 1260 is 36, the number of prime factors of 1260 is 6 (2, 2, 3, 3, 5, 7) and 36 = 6 * 6.

Maple

with(numtheory): P:=proc(q) local k, n; for n from 2 to q do for k from 1 to q do
if tau(k)=n*bigomega(k) then print(k); break; fi; od; od; end: P(10^9);

Mathematica

a[n_] := Block[{k = 2}, While[DivisorSigma[0, k]/PrimeOmega[k] != n, k++];
k]; a /@ Range[2, 10] (* Giovanni Resta, Nov 16 2016 *)

Prog

(PARI) a(n) = my(k=2); while(numdiv(k)!=n*bigomega(k), k++); k \\ Felix Fröhlich, Nov 17 2016

Crossrefs

Cf. A000005, A001222, A275816.

Sequence in context: A087004 A328859 A141055 * A048541 A067739 A187626

Adjacent sequences: A275816 A275817 A275818 * A275820 A275821 A275822

Keyword

nonn

Author

Paolo P. Lava, Nov 15 2016

Extensions

a(11)-a(31) from Giovanni Resta, Nov 16 2016

Status

approved