A365884 Numbers k such that k and k+1 are both terms of A365883.

27, 188, 459, 620, 675, 836, 1107, 1268, 1323, 1484, 1755, 1916, 1971, 2132, 2403, 2564, 2619, 2780, 3051, 3124, 3212, 3267, 3428, 3699, 3860, 3915, 4076, 4347, 4508, 4563, 4724, 4995, 5156, 5211, 5372, 5643, 5804, 5859, 6020, 6291, 6452, 6507, 6668, 6939, 7100

Offset: 1

Author

Amiram Eldar, Sep 22 2023

Keywords

• nonn
• easy

Comments

The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 1, 6, 63, 623, 6216, 62157, 621565, 6215645, 62156450, 621564494, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00621564... .

Examples

			27 = 3^3 is a term since its least prime factor, 3, is equal to its exponent, and also the least prime factor of 28 = 2^2 * 7, 2, is equal to its exponent.
		

Links

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

Crossrefs

Subsequence of A365883 and A365890.

A365885 is a subsequence.

Programs

Mathematica

q[n_] := Equal @@ FactorInteger[n][[1]]; consec[kmax_] := Module[{m = 1, c = Table[False, {2}], s = {}}, Do[c = Join[Rest[c], {q[k]}]; If[And @@ c, AppendTo[s, k - 1]], {k, 1, kmax}]; s]; consec[7200]

PARI

lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = #Set(factor(k)[1,]) == 1; if(q1 && q2, print1(k-1, ", ")); q1 = q2);}