%I #11 Feb 20 2024 10:44:16

%S 4,27,54,108,216,432,864,1728,3125,3456,6250,6912,9375,12500,13824,

%T 18750,25000,27648,28125,37500,50000,55296,56250,75000,84375,100000,

%U 110592,112500,150000,168750,200000,221184,225000,253125,300000,337500,400000,442368,450000

%N Numbers k such that A006530(k) = A071178(k).

%C Union of {4}, numbers of the form 3^3 * 2^k (k >= 0), and the sequence of sets of numbers of the form p^p * k, where k is a p-smooth number (number not divisible by any prime > p), for primes p >= 3.

%H Amiram Eldar, <a href="/A370492/b370492.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{n>=1} 1/a(n) = Sum_{k>=1} 1/(prime(k)^prime(k) * Product_{i=1..k-1} (1 - 1/prime(i))) = 0.32503862758571995411... .

%e 54 = 2 * 3^3 is a term since A006530(54) = A071178(54)= 3.

%t Select[Range[2, 10^6], Equal @@ FactorInteger[#][[-1, ;;]] &]

%o (PARI) is(n)={my(f = factor(n), m = #f~); n > 1 && f[m,1] == f[m,2];}

%Y Cf. A006530, A071178.

%Y Subsequence of A370493.

%Y Subsequences: A051674, A072694, A076265.

%K nonn

%O 1,1

%A _Amiram Eldar_, Feb 20 2024