A354219 Primes p such that the number of distinct prime factors omega of the product of the composite numbers between p and the next prime after p sets a new record.

3, 5, 7, 13, 19, 31, 53, 73, 89, 113, 211, 293, 523, 887, 1129, 1327, 4297, 4831, 5351, 5591, 8467, 12853, 15683, 19609, 25471, 31397, 134513, 155921, 338033, 360653, 370261, 492113, 1349533, 1357201, 1561919, 2010733, 4652353, 8421251, 11113933, 15203977, 17051707

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Example

a(6) = 31, because the first product of consecutive composites with 6 primes in its squarefree kernel is P = 32*33*34*35*36 with rad(P) = 2*3*5*7*11*17 = 39270, whereas the interval starting after A354217(6) = 23 leads only to 5 distinct factors, i.e., rad(24*25*26*27*28) = 2*3*5*7*13, not sufficient to beat the record set by the composites after a(5) = A354217(5) = 19 with rad(20*21*22) = 2*3*5*7*11.

Mathematica

s = Array[PrimeNu[Times @@ FactorInteger[Times @@ Range[#1 + 1, #2 - 1]][[All, 1]] & @@ Map[Prime, # + {0, 1}]] &, 10^4]; Prime@ Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, May 20 2022 *)

Crossrefs

A354220 provides the corresponding values of omega.

Cf. A001221, A076978, A354217.

Sequence in context: A067829 A084696 A352952 * A330222 A154700 A187872

Adjacent sequences: A354216 A354217 A354218 * A354220 A354221 A354222

Keyword

nonn

Author

Hugo Pfoertner, May 20 2022

Status

approved