A144976 Nonsquarefree numbers k such that k is divisible by the maximal exponent in the prime factorization of k.

4, 12, 16, 18, 20, 24, 27, 28, 36, 44, 48, 50, 52, 54, 60, 68, 72, 76, 80, 84, 90, 92, 98, 100, 108, 112, 116, 120, 124, 126, 132, 135, 140, 144, 148, 150, 156, 160, 164, 168, 172, 176, 180, 188, 189, 192, 196, 198, 204, 208, 212, 216, 220, 228, 234, 236, 240, 242, 244, 252, 256, 260, 264, 268, 270, 272

Offset: 1

Author

Giovanni Teofilatto, Sep 28 2008

Keywords

• nonn

Comments

The asymptotic density of this sequence is A336065 - A059956 = 0.24103009315... . - Amiram Eldar, Jan 05 2024

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A013929 and A336064.

Cf. A059956, A137257, A336065.

Programs

Maple

A051903 := proc(n) local a,ifs,p,e; a := 1 ; max( seq(op(2,p),p=ifactors(n)[2]) ); end: isA013929 := proc(n) RETURN( not isprime(n) and A051903(n) > 1 ) ; end: isA144976 := proc(n) RETURN( isA013929(n) and (n mod A051903(n)) = 0 ); end: for n from 4 to 400 do if isA144976(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Oct 24 2008

Mathematica

Select[Range[300],!SquareFreeQ[#]&&Divisible[#,Max[FactorInteger[#][[All,2]]]]&] (* Harvey P. Dale, Jul 01 2017 *)

PARI

is(n) = {my(e = factor(n)[, 2], emax); if(n == 1, 0, emax = vecmax(e); emax > 1 && !(n % emax));} \\ Amiram Eldar, Jan 05 2024

Formula

{A013929(i): A051903(A013929(i)) | A013929(i)}. - R. J. Mathar, Oct 24 2008

Extensions

Adapted definition, inserted 18, 20 and extended. - R. J. Mathar, Oct 24 2008