A348101 Starts of runs of 5 consecutive numbers that have an equal number of unitary and nonunitary prime divisors (A348097).

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

Amiram Eldar, Table of n, a(n) for n = 1..500

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

Adjacent sequences: A348098 A348099 A348100 * A348102 A348103 A348104

Keyword

nonn

Author

Amiram Eldar, Sep 30 2021

Status

approved