A290051 - OEIS

A290051

Least k > 1 such that the set of distinct prime divisors of k is equal to the set of distinct prime divisors of sigma_n(k) where sigma_n (k) is result of applying sum-of-divisors function n times to k.

%I #22 Aug 08 2017 22:04:19

%S 6,2,294,2,126,112,310,14,150,840,3200,98,45360,10500,57120,40320,

%T 242250,9548,21839790,3756480,200425680,678810,1359540

%N Least k > 1 such that the set of distinct prime divisors of k is equal to the set of distinct prime divisors of sigma_n(k) where sigma_n (k) is result of applying sum-of-divisors function n times to k.

%C a(24) > 10^9.

%e a(3) = 294 because sigma(sigma(sigma(2*3*7^2))) = 2^5*3*7^2 and 2*3*7^2 = 294 is the least number with this property.

%t f[n_] := Block[{k = 2}, While[ Transpose[ FactorInteger[ Nest[ DivisorSigma[1, #] &, k, n]]][[1]] != Transpose[ FactorInteger[ k]][[1]], k += 2]; k]; (* _Robert G. Wilson v_, Aug 03 2017 *)

%Y Cf. A000203, A027598.

%K nonn,more

%O 1,1

%A _Altug Alkan_, Aug 03 2017

%E a(10)-a(23) from _Giovanni Resta_, Aug 03 2017