A365890 Numbers k such that k and k+1 are both terms of A365889.

27, 188, 459, 620, 675, 783, 836, 944, 1107, 1268, 1323, 1484, 1647, 1755, 1808, 1916, 1971, 2132, 2240, 2403, 2564, 2619, 2780, 3051, 3124, 3212, 3267, 3375, 3428, 3536, 3644, 3699, 3860, 3915, 4076, 4239, 4347, 4400, 4508, 4563, 4671, 4724, 4995, 5103, 5156

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, 8, 88, 862, 8607, 86044, 860407, 8604097, 86041005, 860410068, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00860410... .

Examples

			27 = 3^3 is a term since its least prime factor, 3, divides its exponent, 3, and the least prime factor of 28 = 2^2 * 7, 2, also divides its exponent, 2.
783 = 3^3 * 29 is a term since its least prime factor, 3, divides its exponent, 3, and the least prime factor of 784 = 2^4 * 7^2, 2, also divides its exponent, 4.
		

Links

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

Crossrefs

Subsequence of A365889.

Subsequences: A365884, A365891.

Programs

Mathematica

q[n_] := Divisible @@ Reverse[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[6000]

PARI

is(n) = {my(f = factor(n)); n > 1 && !(f[1, 2] % f[1, 1]);}
lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = is(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}