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A275816 Least number k such that the number of its divisors is n times, with n>1, the number of its prime factors, counted without multiplicity. 2
2, 4, 8, 16, 32, 64, 128, 256, 432, 1024, 864, 4096, 1728, 2592, 3456, 65536, 6912, 262144, 10368, 14400, 27648, 4194304, 21600, 32400, 110592, 50400, 43200, 268435456, 64800, 1073741824, 86400, 230400, 1769472, 129600, 151200, 68719476736, 7077888, 921600 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

The number of divisors of p^(n-1) is n times the number of prime factors of p^(n-1), where p is prime. It means that a solution exists for every n>1.

LINKS

Giovanni Resta, Table of n, a(n) for n = 2..100

FORMULA

Least solution k of the equation A000005(k) = n * A001221(k).

EXAMPLE

a(10) = 432 because the number of divisors of 432 is 20, the number of different prime factors of 432 is 2 (2, 3), and 20 = 10 * 2.

MAPLE

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

if tau(k)=n*nops(factorset(k)) then print(k); break; fi; od; od; end: P(10^9);

MATHEMATICA

a[n_] := Block[{k = 2}, If[PrimeQ[n], 2^n/2, While[ DivisorSigma[0, k]/ PrimeNu[k] != n, k++]; k]]; a /@ Range[2, 25] (* Giovanni Resta, Nov 16 2016 *)

CROSSREFS

Cf. A000005, A001221, A275819.

Sequence in context: A252757 A230579 A009694 * A097000 A285894 A271481

Adjacent sequences:  A275813 A275814 A275815 * A275817 A275818 A275819

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, Nov 15 2016

EXTENSIONS

a(29)-a(39) from Giovanni Resta, Nov 16 2016

STATUS

approved

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Last modified June 2 06:12 EDT 2020. Contains 334767 sequences. (Running on oeis4.)