A348121 -id:A348121 - cp's OEIS frontend

A348122 Numbers k such that k and k+1 both have more nonunitary than unitary prime divisors (A348121).

8, 288, 360, 675, 1224, 1331, 1368, 2196, 2400, 2600, 2808, 3024, 5328, 6075, 6859, 9408, 9800, 10647, 11448, 12167, 16128, 17199, 19844, 20448, 21024, 23275, 25920, 26568, 26900, 28899, 29791, 33524, 38024, 38808, 39600, 40400, 41624, 42875, 45324, 46224, 46475

Offset: 1

Amiram Eldar, Oct 01 2021

nonn

			8 is a term since 8 = 2^3 has one nonunitary prime divisor, 2, and no unitary prime divisors, and 8 + 1 = 9 = 3^2 has one nonunitary prime divisor, 3, and no unitary prime divisors.

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

Subsequence of A348121.
A060355 is a subsequence.
Similar sequence: A348119.

q[n_] := 2*Count[(e = FactorInteger[n][[;; , 2]]), 1] < Length[e]; Select[Range[5*10^5], q[#] && q[# + 1] &]

A348123 Starts of runs of 3 consecutive numbers that have more nonunitary than unitary prime divisors (A348121).

Original entry on oeis.org

959075, 1492775, 5038523, 5132699, 9905300, 38002831, 40441023, 50473575, 67706631, 80108775, 81355923, 109436875, 128428999, 165332223, 169067491, 171024111, 178878175, 196224075, 224042624, 247529574, 274205223, 279645399, 282880575, 284267374, 299969423, 329523775

Offset: 1

Amiram Eldar, Oct 01 2021

nonn

There are no runs of 4 consecutive numbers below 2.4*10^10.

It is conjectured that there are no runs of 3 consecutive numbers that are powerful (A001694), but if they do exist, their starts are contained in this sequence.

			959075 is a term since 959075 = 5^2 * 13^2 * 227, 959075 + 1 = 959076 = 2^2 * 3^2 * 26641 and 959075 + 2 = 959077 = 7^2 * 23^2 * 37 all have 2 nonunitary prime divisors and only 1 unitary prime divisor.

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

Subsequence of A348121 and A348122.
Cf. A001694.
Similar sequence: A348120.

q[n_] := 2*Count[(e = FactorInteger[n][[;; , 2]]), 1] < Length[e]; v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k - 2]], {k, 4, 5*10^7}]; seq

cp's OEIS Frontend

A348122 Numbers k such that k and k+1 both have more nonunitary than unitary prime divisors (A348121).

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