A364266 The first term in a chain of at least 3 consecutive numbers each with exactly 5 distinct prime factors.

1042404, 3460280, 3818828, 3998664, 4638984, 4991964, 5540248, 5701254, 5715500, 5964958, 6772050, 6794084, 7237384, 7453964, 7459088, 7745318, 7757034, 7993194, 8083634, 8153430, 8168194, 8273628, 8340834, 8340980, 8414756, 8486994, 8698898, 8722634, 8758904

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

a(1) = A087978(3).

{k: A001221(k) = A001221(k+1) = A001221(k+2) = 5}. - R. J. Mathar, Jul 18 2023

Example

1042404 = 2^2*3*11*53*149, 1042405 = 5*6*143*29*79 and 1042406 = 2*17*23*31*43 each have 5 distinct prime factors, so 1042404 is in the sequence.

Maple

omega := proc(n)
    nops(numtheory[factorset](n)) ;
end proc:
for k from 1 do
    if omega(k) = 5 then
        if omega(k+1) = 5 then
            if omega(k+2) = 5 then
                print(k) ;
            end if;
        end if;
    end if;
end do:

Crossrefs

Cf. A192203 (subsequence for squarefree triples). Subsequence of A140079 (2 consec.) and of A006073.

Cf. A364308 (3 dist. factors), A364309 (4 dist. factors), A364265 (6 dist. factors), A001221.

Sequence in context: A030084 A030092 A237073 * A179448 A289825 A013696

Adjacent sequences: A364263 A364264 A364265 * A364267 A364268 A364269

Keyword

nonn

Author

R. J. Mathar, Jul 16 2023

Status

approved