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A342029
Starts of runs of 3 consecutive numbers that have mutually distinct exponents in their prime factorization (A130091).
8
1, 2, 3, 7, 11, 16, 17, 18, 23, 27, 43, 47, 48, 52, 71, 79, 96, 97, 107, 135, 147, 151, 162, 171, 191, 241, 242, 243, 331, 351, 359, 367, 387, 423, 431, 486, 507, 539, 547, 567, 575, 576, 599, 603, 639, 907, 927, 1051, 1107, 1123, 1151, 1215, 1249, 1250, 1323
OFFSET
1,2
LINKS
Kevser Aktaş and M. Ram Murty, On the number of special numbers, Proceedings - Mathematical Sciences, Vol. 127, No. 3 (2017), pp. 423-430; alternative link.
EXAMPLE
2 is a term since 2, 3 and 4 = 2^2 all have a single exponent in their prime factorization.
4 is not a term since in the run {4, 5, 6} the third member 6 = 2*3 has two equal exponents (1) in its prime factorization.
MATHEMATICA
q[n_] := Length[(e = FactorInteger[n][[;; , 2]])] == Length[Union[e]]; v = q /@ Range[3]; seq = {}; Do[If[And @@ v, AppendTo[seq, k - 3]]; v = Join[Rest[v], {q[k]}], {k, 4, 1500}]; seq
CROSSREFS
Subsequence of A130091 and A342028.
Subsequences: A342030, A342031.
Sequence in context: A189374 A180516 A100963 * A368403 A361857 A197636
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 25 2021
STATUS
approved