A370493 Numbers k such that A006530(k) = A051903(k).

4, 24, 27, 54, 72, 108, 160, 216, 480, 800, 896, 1215, 1440, 2400, 2430, 2688, 3125, 4000, 4320, 4480, 4860, 6075, 6250, 6272, 7200, 8064, 9375, 9720, 12000, 12150, 12500, 12960, 13440, 15309, 18750, 18816, 19440, 20000, 21600, 22400, 22528, 24192, 24300, 25000

Offset: 1

Author

Amiram Eldar, Feb 20 2024

Keywords

• nonn

Examples

			72 = 2^3 * 3^2 is a term since A006530(72) = A051903(72) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A002110, A006530, A051903, A017665, A017666.

Subsequences: A051674, A100042, A370492.

Programs

Mathematica

q[n_] := Module[{f = FactorInteger[n]}, Max[f[[;; , 2]]] == f[[-1, 1]]]; Select[Range[2, 25000], q]

PARI

is(n)={my(f = factor(n), p = f[,1], e = f[,2]); n > 1 && p[#p] == vecmax(e);}

Formula

Sum_{n>=1} 1/a(n) = Sum_{k>=1} ((Sum_{i=1..prime(k)-1} 1/p^i) * (s(p(k-1)^prime(k)) - s(p(k-1)^(prime(k)-1))) + s(p(k-1)^prime(k))/prime(k)^prime(k)) = 0.39239336056178266729..., where s(k) = sigma_{-1}(k) = A017665(k)/A017666(k), and p(k) = prime(k)# = A002110(k).