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A365864
Numbers k such that k and k+1 are both divisible by the square of their least prime factor.
3
8, 24, 27, 44, 48, 63, 80, 99, 116, 120, 124, 135, 152, 168, 171, 175, 188, 207, 224, 243, 260, 275, 279, 288, 296, 315, 324, 332, 343, 351, 360, 368, 387, 404, 423, 424, 440, 459, 475, 476, 495, 512, 528, 531, 539, 548, 567, 575, 584, 603, 620, 624, 636, 639
OFFSET
1,1
COMMENTS
Numbers k such that k and k+1 are both terms of A283050.
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 8, 82, 802, 8009, 80078, 800900, 8009533, 80097354, 800979764, 8009809838, ... . Apparently, the asymptotic density of this sequence exists and equals 0.08009... .
LINKS
EXAMPLE
8 is a term since 2 is the least prime factor of 8 and 8 is divisible by 2^2 = 4, and 3 is the least prime factor of 9 and 9 is divisible by 3^3 = 9.
MATHEMATICA
q[n_] := FactorInteger[n][[1, -1]] >= 2; 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[640]
PROG
(PARI) lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = factor(k)[1, 2] >= 2; if(q1 && q2, print1(k-1, ", ")); q1 = q2); }
CROSSREFS
Cf. A067029.
Subsequence of A068781 and A283050.
A365865 is a subsequence.
Sequence in context: A175496 A048109 A068781 * A212861 A333961 A038524
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 21 2023
STATUS
approved