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A365890
Numbers k such that k and k+1 are both terms of A365889.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 22 2023
STATUS
approved