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

Author

Amiram Eldar, Sep 30 2021

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A348097, A348098 and A348099.

Cf. A335398.

Programs

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