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

1,1

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... .

Links

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

Example

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.

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]

Prog

(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); }

Crossrefs

Subsequence of A365889.

Subsequences: A365884, A365891.

Sequence in context: A258637 A228463 A000499 * A365884 A042416 A216108

Adjacent sequences: A365887 A365888 A365889 * A365891 A365892 A365893

Keyword

nonn,easy

Author

Amiram Eldar, Sep 22 2023

Status

approved