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A348101
Starts of runs of 5 consecutive numbers that have an equal number of unitary and nonunitary prime divisors (A348097).
1
906596, 12133672, 19293208, 23542000, 25793449, 70289224, 77449300, 130397524, 316377124, 359762848, 371355172, 395284372, 415670200, 527032924, 600284788, 642788072, 730243348, 746696248, 754642996, 792007675, 1153139048, 1153702448, 1338997372, 1359156472
OFFSET
1,1
COMMENTS
1744218747 is the least start of a run of 6 consecutive numbers. The next such run starts with 73840265847.
LINKS
EXAMPLE
906596 is a term since 906596 = 2^2 * 226649, 906596 + 1 = 906597 = 3^2 * 100733, 906596 + 2 = 906598 = 2 * 7^2 * 11 * 29^2, 906596 + 3 = 906599 = 71 * 113^2 and 906596 + 4 = 906600 = 2^3 * 3 * 5^2 * 1511 all have the same number of unitary and nonunitary prime divisors.
MATHEMATICA
q[n_] := n == 1 || Count[(e = FactorInteger[n][[;; , 2]]), 1] == Length[e]/2; v = q /@ Range[5]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 4]], {k, 6, 3*10^7}]; seq
CROSSREFS
Subsequence of A348097, A348098, A348099 and A348100.
Cf. A335399.
Sequence in context: A250542 A251799 A348078 * A179735 A015333 A141461
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 30 2021
STATUS
approved