A348100 Starts of runs of 4 consecutive numbers that have an equal number of unitary and nonunitary prime divisors (A348097).

56347, 906596, 906597, 1090250, 1141550, 1243275, 4972372, 5684822, 6288488, 6379748, 6486325, 6907974, 7480447, 8587249, 9129248, 11112173, 12133672, 12133673, 13852924, 14185448, 17519948, 19293208, 19293209, 19751750, 20738672, 21560848, 21721796, 21959350

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

56347 is a term since 56347 = 29^2 * 67, 56347 + 1 = 56348 = 2^2 * 14087, 56347 + 2 = 56349 = 3^3 * 2087 and 56347 + 3 = 56350 = 2 * 5^2 * 7^2 * 23 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[4]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 3]], {k, 5, 1.3*10^6}]; seq

Crossrefs

Subsequence of A348097, A348098 and A348099.

Cf. A335398.

Sequence in context: A198165 A244294 A234488 * A184613 A202433 A329270

Adjacent sequences: A348097 A348098 A348099 * A348101 A348102 A348103

Keyword

nonn

Author

Amiram Eldar, Sep 30 2021

Status

approved