A370492 Numbers k such that A006530(k) = A071178(k).

4, 27, 54, 108, 216, 432, 864, 1728, 3125, 3456, 6250, 6912, 9375, 12500, 13824, 18750, 25000, 27648, 28125, 37500, 50000, 55296, 56250, 75000, 84375, 100000, 110592, 112500, 150000, 168750, 200000, 221184, 225000, 253125, 300000, 337500, 400000, 442368, 450000

Offset: 1

Author

Amiram Eldar, Feb 20 2024

Keywords

• nonn

Comments

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.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A071178.

Subsequence of A370493.

Subsequences: A051674, A072694, A076265.

Programs

Mathematica

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

PARI

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

Formula

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... .